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As well known, low rank representation method (LRR) has obtained promising performance for subspace clustering, and many LRR variants have been developed, which mainly solve the three problems existing in LRR: 1) Problem of mean calculation; 2) Problem of deviating from the real low rank solution; 3) Problem of high computation cost on the large-scale data. In this paper, we first propose a universal LRR method referring to the first two problems. More specifically, we introduce the ability of removing the optimal mean automatically into LRR and extend it to a Schatten p-norm minimization problem. Then, referring to the third problem, we reformulate the universal LRR version as an equivalent fast optimization version by removing the null space of data. More importantly, the effective theory proof is proposed to guarantee that the fast optimization method can dramatically improve the algorithmic computation efficiency on the large-scale data but without any loss of information. Finally, experimental results demonstrate the effectiveness and efficiency of the proposed method.

Since polar codes are capacity-achieving codes, there have been various research works devoted to devising efficient implementation methods as well as improving error-correction performance. Since quantization is a critical implementation issue, in this paper, a nonuniform quantization method is proposed for the successive cancellation (SC) decoder of polar codes, which finds quantization boundary values based on the analysis of various quantization levels over the additive white Gaussian noise channel. Since low computational complexity, high reliability, and efficient memory management are required in the next-generation communication and memory systems, 2–4 bit precision levels are mainly considered in the proposed nonuniform quantization method. Depending on the presence of erasure, quantization levels are divided into three types, and the message alphabets and update rules are derived for each type. Also, a construction method of polar codes suitable for the proposed nonuniform-quantized SC decoder is proposed, which simultaneously determines the information set and the quantization boundary values based on the density evolution analysis and an upper bound of the block error probability. To determine quantization boundary values, a multivariate objective function is defined and an iterative coarse-to-fine search algorithm to minimize this objective function is proposed. In addition, a scaling method of quantizer output values is proposed when the number of quantization levels of quantizer is smaller than the number of quantization levels of decoder. Finally, simulation results confirm that the proposed nonuniform-quantized SC decoder shows better error-correction performance, lower decoding complexity, and higher memory efficiency compared to the best known uniform-quantized SC decoder.

Wavelet tight frames have been actively investigated for various image restoration problems. In this paper, we introduce an analysis-sparsity model via $\ell _2$ -relaxed truncated $\ell _0$ regularization and nonlocal estimation, and the resulted nonconvex minimization problem is tackled by a proximal alternating minimization strategy. Numerical experiments demonstrate that the proposed algorithm is superior to many popular methods in both objective and perceptual quality.

In the paper, we study the minimization problem of a non-convex sparsity promoting penalty function $$P_{a}(x)=\sum_{i=1}^{n}p_{a}(x_{i})=\sum_{i=1}^{n}\frac{a|x_{i}|}{1+a|x_{i}|}$$ in compressed sensing, which is called fraction function. Firstly, we discuss the equivalence of $\ell_{0}$ minimization and fraction function minimization. It is proved that there corresponds a constant $a^{**}>0$ such that, whenever $a>a^{**}$, every solution to $(FP_{a})$ also solves $(P_{0})$, that the uniqueness of global minimizer of $(FP_{a})$ and its equivalence to $(P_{0})$ if the sensing matrix $A$ satisfies a restricted isometry property (RIP) and, last but the most important, that the optimal solution to the regularization problem $(FP_{a}^\lambda)$ also solves $(FP_{a})$ if the certain condition is satisfied, which is similar to the regularization problem in convex optimal theory. Secondly, we study the properties of the optimal solution to the regularization problem $(FP^{\lambda}_{a})$ including the first-order and the second optimality condition and the lower and upper bound of the absolute value for its nonzero entries. Finally, we derive the closed form representation of the optimal solution to the regularization problem ($FP_{a}^{\lambda}$) for all positive values of parameter $a$, and propose an iterative $FP$ thresholding algorithm to solve the regularization problem $(FP_{a}^{\lambda})$. We also provide a series of experiments to assess performance of the $FP$ algorithm, and the experiment results show that, compared with soft thresholding algorithm and half thresholding algorithms, the $FP$ algorithm performs the best in sparse signal recovery with and without measurement noise., Comment: 12 pages

Subspace clustering has been widely applied to detect meaningful clusters in high-dimensional data spaces. And the sparse subspace clustering (SSC) obtains superior clustering performance by solving a relaxed ℓ0-minimization problem with ℓ1-norm. Although the use of ℓ1-norm instead of the ℓ0 one can make the object function convex, it causes large errors on large coefficients in some cases. In this paper, we study the sparse subspace clustering algorithm based on a nonconvex modeling formulation. Specifically, we introduce a nonconvex pseudo-norm that makes a better approximation to the ℓ0-minimization than the traditional ℓ1-minimization framework and consequently finds a better affinity matrix. However, this formulation makes the optimization task challenging due to that the traditional alternating direction method of multipliers (ADMM) encounters troubles in solving the nonconvex subproblems. In view of this, the reweighted techniques are employed in making these subproblems convex and easily solvable. We provide several guarantees to derive the convergence results, which proves that the nonconvex algorithm is globally convergent to a critical point. Experiments on two real-world problems of motion segmentation and face clustering show that our method outperforms state-of-the-art techniques.

It is widely known that the classic total variation(TV) model has been proven to be very effective in preserving sharp edges. However, the TV model suffers from the staircase effects which produce blocking artifacts in the restored images. In this paper, we propose a new hybrid regularization model by combining non-convex second order total variation with wavelet transform to restrain staircase effects and protect some details of the images. To compute the new model effectively, we propose an alternating minimization method for recovering images from the blurry and noisy observations. The new model is first transformed into several sub-problems, and the generalized iterated shrinkage algorithm, the Fourier transform method and projection method are used to solve these sub-problems, respectively. Numerical experiments show that the proposed model can restrain blocking artifacts while projecting sharp edges, and the restoration quality outperforms several state-of-the-art methods.

A sound field reproduction method based on the spherical wavefunction expansion of sound fields is proposed, which can be flexibly applied to various array geometries and directivities. First, we formulate sound field synthesis as a minimization problem of some norm on the difference between the desired and synthesized sound fields, and then the optimal driving signals are derived by using the spherical wavefunction expansion of the sound fields. This formulation is closely related to the mode-matching method; a major advantage of the proposed method is the optimal weight on the mode determined according to the norm to be minimized instead of the empirical truncation in the mode-matching method. We also provide some examples of norms and their corresponding weights in analytical forms. Both interior and exterior sound field reproduction are considered in the proposed method, and some applications, such as multizone reproduction and interior reproduction with exterior cancellation, are also discussed. Numerical simulation results indicated that higher reproduction accuracy can be achieved by the proposed method than by the current pressure-matching and mode-matching methods.

With the increasing penetration of electric vehicles (EVs) and various user preferences, charging stations often provide several different charging modes to satisfy the various requirements of EVs. How to effectively utilize the charging capacity to minimize the service dropping rate is a pressing and open issue for charging stations. Given that EV owners are price-sensitive to the charging modes, we intend to design an optimal pricing scheme to minimize the service dropping rate of the charging station. First, we formulate the operation of a dual-mode charging station as a queuing network with multiple servers and heterogeneous service rates, and analyze the relationship between the service dropping rate of the charging station and the selections of EVs. Then, we formulate a customer attrition minimization problem to minimize the number of EVs that leave the charging station without being charged and propose an optimal pricing approach to guide and coordinate the charging processes of EVs in the charging station. The simulation has been conducted to evaluate the performance of the proposed charging scheduling scheme and show the efficiency of the proposed pricing scheme.

In sparse recovery, a sparse signal ${\mathbf x}\in \mathbb {R}^N$ with $K$ nonzero entries is to be reconstructed from a compressed measurement $\mathbf y=Ax$ with ${\mathbf A}\in \mathbb {R}^{M\times N}$ ( $M ). The $\ell _p$ $(0\leq p pseudonorm has been found to be a sparsity inducing function superior to the $\ell _1$ norm, and the null space constant (NSC) and restricted isometry constant (RIC) have been used as key notions in the performance analyses of the corresponding $\ell _p$ -minimization. In this paper, we study sparse recovery conditions and performance bounds for the $\ell _p$ -minimization. We devise a new NSC upper bound that outperforms the state-of-the-art result. Based on the improved NSC upper bound, we provide a new RIC upper bound dependent on the sparsity level $K$ as a sufficient condition for precise recovery, and it is tighter than the existing bound for small $K$ . Then, we study the largest choice of $p$ for the $\ell _p$ -minimization problem to recover any $K$ -sparse signal, and the largest recoverable $K$ for a fixed $p$ . Numerical experiments demonstrate the improvement of the proposed bounds in the recovery conditions over the up-to-date counterparts.

Low-rank modeling-based moving object detection approaches proposed so far use fixed ${{\boldsymbol{l}}_1}$ -norm penalty to capture the sparse nature of foreground in video, and thus, hardly adapt readily to the statistical variability of underlying foreground pixels in dynamic background. Additionally, they ignore the spatial continuity prior among the neighbor foreground pixels. Consequently, they cannot offer a satisfactory performance in practical dynamic background. In this letter, we present a unified regularization framework, namely ${{\boldsymbol{l}}_{1/2}}$ -norm and spatial continuity regularized low-rank approximation (SCLR- ${{\boldsymbol{l}}_{1/2}}$ ), to solve this problem. First, in order to promote accuracy, we introduce an ${{\boldsymbol{l}}_{1/2}}$ constraint into the framework. Second, to guarantee the continuity among the neighbor foreground pixels, we introduce a spatial continuity regularization term, motivated by total variation. Finally, we generalize our framework to the ${{\boldsymbol{l}}_{\boldsymbol{q}}}$ -norm penalized case (SCLR- ${{\boldsymbol{l}}_{\boldsymbol{q}}}$ ). By adjusting the shrinkage parameter ${\boldsymbol{q}}$ , the framework gets better flexibility to choose a reasonable sparse domain. To deal with the present constrained minimization problem, the augmented Lagrange multiplier method is employed and extended with the help of the alternating direction minimizing strategy. Experimental results show that the proposed method outperforms some state-of-the-art algorithms especially for the cases with dynamic backgrounds.

Transform learning has been proposed as a new and effective formulation for analysis dictionary learning, where the $\ell _{0}$ norm or the $\ell _{1}$ norm are generally used as sparsity constraint. The sparse solutions can be obtained by the hard thresholding or the soft thresholding. The hard thresholding is actually a greedy algorithm, which only obtains the approximate solutions; while the soft thresholding has a certain bias for the large elements. In this paper, we propose to employ the $log$ regularizer instead of the $\ell _{0}$ norm and the $\ell _{1}$ norm in the overcomplete transform learning problem. Our minimization problem is nonconvex due to the $log$ regularizer. We propose to employ a simple proximal alternating minimization method, where a closed-form solution of the $log$ function could be obtained based on the proximal operator. Hence, an efficient and fast overcomplete transform learning algorithm is developed, which iterates based on the analysis coding stage and the transform update stage. The proposed algorithm can obtain sparser solutions and more accurate results from the theoretical analysis. Numerical experiments verify that the proposed algorithm outperforms existing transform learning approaches with the $\ell _{0}$ norm or the $\ell _{1}$ norm. Furthermore, the proposed algorithm is on par with the state-of-the-art image denoising algorithms.

Objective: This paper introduces methods to automate preoperative planning of fibular segmentation and placement for mandibular reconstruction with fibular flaps. Methods: Preoperative virtual planning for this type of surgery has been performed by manual adjustment of many parameters, or based upon a single feature of the reconstruction. We propose a novel planning procedure formulated as a non-convex minimization problem of an objective function using the multilateral shape descriptors. Results: A retrospective study was designed and 120 reconstruction plans were reproduced using computed tomography images with oral surgeons. The proposed automated planning model was quantitatively compared with both the existing model and the surgeons’ plans. Conclusion: The results show that the developed framework attains stable automated planning that agrees with the surgeons’ decisions. Significance: This method addresses trade-off problems between symmetric reconstruction and restoration of the native contour of the mandible.

The increasing penetration of renewable energy sources (RES) requires more flexibility resources (FR), such as thermal units and storages. FR kept in the system can help accommodate the uncertainties from RES. The challenge is how the system can survive when the RES level is very high. In this paper, RESs are considered as full-role market participants. They can bid in the day-ahead market, and the powers they deliver to the market are controllable up to their maximum available powers. Therefore, RESs are effectively dispatchable and can function as FR. To integrate dispatchable renewables, a two-stage robust unit commitment (UC) and dispatch model is established. In the first stage, a base UC and dispatch is determined. In the second stage, all FRs including RESs are used to accommodate the uncertainties, which is a mixed-integer programming (MIP) problem. It is proved that the solution to the max–min problem can be identified directly whether the strong duality holds or not for the inner minimization problem. The solution robustness can be guaranteed by considering only one extra scenario. Numerical results show the effectiveness of the proposed model and its advantages over the traditional robust UC model with high-level RES penetration.

The array diagnosis technique based on nonconvex compressed sensing approach is introduced for a uniform linear array. In this sense, ${l_p}$ minimization problem with $p is proposed for array diagnosis problem and it is solved using a weighted least squares approach. The proposed approach locates the faulty elements using less far-field measurements compared to the standard ${l_1}$ minimization.

The literature on sparse recovery often adopts the ${\ell _p}$ “norm” ( $p \in [0,1]$ ) as the penalty to induce sparsity of the signal satisfying an underdetermined linear system. The performance of the corresponding ${\ell _p}$ minimization problem can be characterized by its null space constant. In spite of the NP-hardness of computing the constant, its properties can still help in illustrating the performance of ${\ell _p}$ minimization. In this letter, we show the strict increase of the null space constant in the sparsity level $k$ and its continuity in the exponent $p$ . We also indicate that the constant is strictly increasing in $p$ with probability 1 when the sensing matrix ${\bf A}$ is randomly generated. Finally, we show how these properties can help in demonstrating the performance of ${\ell _p}$ minimization, mainly in the relationship between the the exponent $p$ and the sparsity level $k$ .

A novel multi-observer passive localization algorithm based on the weighted restricted total least square (WRTLS) is proposed to solve the bearings-only localization problem in the presence of observer position errors. Firstly, the unknown matrix perturbation information is utilized to form the WRTLS problem. Then, the corresponding constrained optimization problem is transformed into an unconstrained one, which is a generalized Rayleigh quotient minimization problem. Thus, the solution can be got through the generalized eigenvalue decomposition and requires no initial state guess process. Simulation results indicate that the proposed algorithm can approach the Cramer-Rao lower bound (CRLB), and the localization solution is asymptotically unbiased.

Two new improved recursive least-squares adaptive-filtering algorithms, one with a variable forgetting factor and the other with a variable convergence factor are proposed. Optimal forgetting and convergence factors are obtained by minimizing the mean square of the noise-free a posteriori error signal. The determination of the optimal forgetting and convergence factors requires information about the noise-free a priori error which is obtained by solving a known L1-L2 minimization problem. Simulation results in system-identification and channel-equalization applications are presented which demonstrate that improved steady-state misalignment, tracking capability, and readaptation can be achieved relative to those in some state-of-the-art competing algorithms.

This work addresses the problem of real-time reconstruction of Dynamic Contrast Enhanced Magnetic Resonance Images (DCE MRI) from partially sampled K-space. The difference image between the current and previous frame is modeled as a rank deficient matrix. It is reconstructed from via nonconvex Schatten-p norm minimization. We develop a FOCUSS (FOCally Under-determined System Solver) based algorithm for solving the said minimization problem. The proposed technique has been compared with state-of-the-art online and offline reconstruction techniques. It yields slightly worse reconstruction results than the offline technique but considerably superior results, both in terms of accuracy and speed compared to the online technique.

There are two key issues in successfully solving the image restoration problem: 1) estimation of the regularization parameter that balances data fidelity with the regularity of the solution and 2) development of efficient numerical techniques for computing the solution. In this paper, we derive a fast algorithm that simultaneously estimates the regularization parameter and restores the image. The new approach is based on the total-variation (TV) regularized strategy and Morozov's discrepancy principle. The TV norm is represented by the dual formulation that changes the minimization problem into a minimax problem. A proximal point method is developed to compute the saddle point of the minimax problem. By adjusting the regularization parameter adaptively in each iteration, the solution is guaranteed to satisfy the discrepancy principle. We will give the convergence proof of our algorithm and numerically show that it is better than some state-of-the-art methods in terms of both speed and accuracy.

We present a low-complexity minimum Linfin-norm adaptive filtering algorithm with sparse updates. A new constrained minimization problem based on the minimum disturbance in the Linfin-norm sense is developed. Solving this minimization problem gives birth to an efficient algorithm which decreases the number of updates as well as the complexity per each iteration. Experimental results comparing the proposed algorithm to the conventional algorithms clearly indicate its good convergence performance with greatly reduced complexity.

This paper describes a new fuzzy satisfaction method using genetic algorithms (GA) for multiobjective problems. First, an unsatisfying function, which has a one-to-one correspondence with the membership function, is introduced for expressing "fuzziness". Next, the multiobjective design problem is transformed into a satisfaction problem of constraints by introducing an aspiration level for each objective. Here, in order to handle the fuzziness involved in aspiration levels and constraints, the unsatisfying function is used, and the problem is formulated as a multiobjective minimization problem of unsatisfaction ratings. Then, a GA is employed to solve the problem, and a new strategy is proposed to obtain a group of Pareto-optimal solutions in which the decision maker (DM) is interested. The DM can then seek a satisfaction solution by modifying parameters interactively according to preferences.

The study of the stability of m-dimensional systems is a difficult one especially when m /spl ges/ 3. There exist only a few results in the literature and unfortunately, there does not exist any practical criterion. In this work, the stability of an m-dimensional system is dealt as a minimization problem of the absolute value of its characteristic polynomial over the boundaries of its variables (i.e., on the m unit circles). This minimization problem is solved by using genetic algorithms (GAs). Using GAs we obtain, in general, better results than other methods of minimization (numerical techniques, neural networks, etc.). Numerical examples are presented.

In this paper, we examine a new design method for two-dimensional (2-D) recursive digital filters using genetic algorithms (GAs). The design of the 2-D filter is reduced to a constrained minimization problem the solution of which is achieved by the convergence of an appropriate GA. Theoretical results are illustrated by a numerical example. Also, comparison with the results of some previous design methods is attempted.

This note studies the problem of minimizing a parameterized convex combination of the overshoot and undershoot of a single-input-single-output (SISO) discrete-time system to a fixed input. We provide a simple condition for the solution existence and characterize the structure of optimal solutions. It is shown that a known l/sub /spl infin// suboptimal scheme also works in our problem. In addition, we make a comparative analysis with the l/sub /spl infin// problem.

This note considers the problem of finding a stable reduced-order model for a given stable model so that its H/sub 2/ model reduction cost differs by less than a prescribed error from the optimal cost, which may or may not be achievable. It is shown that this new version of the long-standing H/sub 2/ optimal model reduction problem can be reduced to a well-posed smooth constrained minimization problem whose global solution is guaranteed to exist. In addition, a globally convergent algorithm in the form of an ordinary differential equation is derived.

This paper addresses a robust controller design for multiinput-multioutput (MIMO) discrete-time systems by approximately solving a constrained mixed H/sup 2/ sensitivity minimization problem. Using some of the digital image restoration techniques and by working in the discrete Fourier transform (DFT) domain, we convert the H/sup 2/ control problem into a constrained vector minimization problem in the l/sup 2/-space. A two-stage solution approach is detailed and the robust controller is constructed. The advantage of using the proposed method is that the l/sup 2/-space solution can be analytically expressed and efficiently calculated via existing multichannel algorithms due to the partially block circular structure of the matrices involved in the DFT domain. The approximation can be made arbitrarily close to the original H/sup 2/ control problem if the number of the DFT points is large. Several examples are given to demonstrate the feasibility of the proposed method.

Typical placement objectives involve reducing net-cut cost or minimizing wirelength. Congestion minimization is the least understood, however, it models routability most accurately. In this paper, we study the congestion minimization problem during placement. First, we show that a global placement with minimum wirelength has minimum total congestion. We show that minimizing wirelength may (and in general, will) create locally congested regions. We test seven different congestion minimization objectives. We also propose a post processing stage to minimize congestion. Our main contribution and results can be summarized as follows. (1) Among a variety of cost functions and methods for congestion minimization (including several currently used in industry), wirelength alone followed by a post processing congestion minimization works the best and is one of the fastest. (2) Cost functions such as a hybrid length plus congestion (commonly believed to be very effective) do not always work very well. (3) Net-centric post-processing techniques are among the best congestion alleviation approaches. (4) Congestion at the global placement level, correlates well with congestion of detailed placement.

The emission-constrained dispatch problem is formulated as a nonlinear constrained minimization problem. Consequently, the solution to the problem gives a continuous relationship between cost and annual emission for SO/sub 2/. It is shown that the power system should be operated at the same value of the Lagrangian multiplier, /spl eta/, in every hour where /spl eta/ is defined as /spl part/(production cost)//spl part/(hourly emission). The addition of /spl eta/ as a proxy cost of emission in the economical dispatch procedure achieves this goal. It is shown that the emission-/spl eta/ relationship obtained by NLCM procedure can be used to make operating decisions, in particular, the trading of allowances. >

This paper is concerned with instantaneous jumps in the state trajectory of a singular system. It is shown that such jumps generically exist at the initial time due to inconsistent initial states. The formula for the jumps is derived, which indicates that the jumps linearly depend on the initial state. Moreover, the set of all initial states which do not cause any state jumps for any output feedback is characterized and is revealed to be a linear subspace. In the meantime, the necessary and sufficient conditions are given for the existence of an output feedback to suppress completely the jumps for a given initial state. Finally, we formulate the problem of designing an output feedback not only to stabilize the plant but also to achieve minimum initial jumps as a minimization problem. >

A method for the recognition of multifont printed characters is proposed, giving emphasis to the identification of structural descriptions of character shapes using prototypes. Noise and shape variations are modeled as series of transformations from groups of features in the data to features in each prototype. Thus, the method manages systematically the relative distortion between a candidate shape and its prototype, accomplishing robustness to noise with less than two prototypes per class, on average. The method uses a flexible matching between components and a flexible grouping of the individual components to be matched. A number of shape transformations are defined, including filling of gaps, so that the method handles broken characters. Also, a measure of the amount of distortion that these transformations cause is given. Classification of character shapes is defined as a minimization problem among the possible transformations that map an input shape into prototypical shapes. Some tests with hand-printed numerals confirmed the method's high robustness level. >

An approach to minimization that is based on a state-of-the-art paradigm for the two-level minimization of functions is presented. Some special properties of relations, in contrast to functions, which must be carefully considered in realizing a high-quality procedure for solving the minimization problem are clarified. An efficient heuristic method to find an optimal sum-of-products representation for a multiple-valued relation is proposed and implemented in the program GYOCRO. It uses multiple-valued decision diagrams (MDDs) to represent the characteristic functions for the relations. Experimental results are presented and compared with previous exact and heuristic Boolean relation minimizers to demonstrate the effectiveness of the proposed method. >

The author presents a technique for synthesizing an antenna pattern with a controlled mean-square sidelobe level and a smallest possible beamwidth. The basic idea is to minimize the mean-square error between the array response and the desired response over a mainlobe width subject to a mean-square sidelobe constraint. This formulation results in a quadratically constrained minimization problem. An efficient numerical technique to obtain the optimum weights is presented. Numerical results showed that, under high interference-to-white-noise ratio, the new design approach performs better, on the average, than the Chebyshev technique, in terms of interference rejection. >

Properties of the solution to the L/sup 2/-sensitivity minimization problem are discussed. In particular, a specific form of the solution is derived together with a bound. This bound gives an insight into the difference between a pure L/sup 2/-sensitivity optimal realization, and a mixed L/sup 2//L/sup 1/-sensitivity optimal one. The question of L/sup 2/-sensitivity balanced truncation is addressed, and a counterexample is presented to show that two main properties associated with model reduction by truncating a Lyapunov balanced realization are lost in the case of L/sup 2/-sensitivity balanced truncation. >

The topological via minimization problem in a two-layer environment is considered. A set of n two-terminal nets in a bounded region is given. The authors attempt to find a homotopy to assign nets to distinct layers so that no two nets on the same layer cross each other and the number of vias is minimized. A recursive approach in which an optimal solution to a two-sided channel routing problem is used as a basis is used to solve this problem optimally. The notion of partition number K of a circle graph is introduced, and the total running time of the via minimization algorithm is shown to be O((n/K)/sup 2K-2/ log (n/K)), where n is the total number of nets. >

A general theory of optimal measurement scheduling for least-squares estimation is developed. The theory is based on the assumption that the cost of a measurement is inversely proportional to the variance of measurement noise, and that it is possible to distribute the total measurement cost arbitrarily among a set of measurements. The theory leads to a nonquadratic minimization problem. An effective algorithm for solving this problem is developed. The theory is applied to the prediction of a discrete-time integrated Wiener process from noisy past samples. >

Linear-quadratic Bolza problems of optimal control with variable end points are considered. Under the strengthened Legendre condition, necessary and sufficient optimality conditions are established, and it is shown that the linear-quadratic Bolza problem of optimal control can be reduced to a quadratic minimization problem in a finite-dimensional space. Simple simulations where solutions of a nonlinear problem can be recovered from solutions of the accessory linear-quadratic problem are indicated. Conjectures regarding sufficient conditions for optimality in nonlinear Bolza problems are included. >

Most of the existing coefficient estimation techniques in the literature for autoregressive (AR) symmetric /spl alpha/-stable (S/spl alpha/S) processes require large amounts of data for efficient estimation. However, in many practical cases, either only a short length of data is available or the data is nonstationary. Motivated by the norm of /spl alpha/-stable variables, the AR model coefficient estimation problem is formulated as an l/sub p/-norm minimization problem, and the interactively reweighted least squares (IRLS) is suggested for the solution. The simulation results indicate superior performance when compared to existing methods, especially when only short length data are available.

This letter presents a new method for optimal placement of phasor measurement units (PMU) for complete power system observability. The optimal PMU placement (OPP) problem is formulated as a quadratic minimization problem with continuous decision variables subject to nonlinear observability constraints. The optimal solution is obtained by an unconstrained nonlinear weighted least squares (WLS) approach. Simulations are conducted on different IEEE systems (14-bus, 30-bus, 57-bus, and 118-bus) to prove the validity of the proposed algorithm.

Currently, symbolic cover minimization is computed using multiple-valued-logic minimization. This problem, however, is computationally intractable, so less accurate heuristics are used. An alternative approach to computationally intractable problems is to reduce their generality so that the simpler problem has a tractable solution. Accordingly, a deterministic approach for the symbolic cover minimization problem for fully input/output (I/O) specified finite state machines (FSMs) is presented. A uniqueness theorem for a hierarchical extension of FSMs is proved, and the theorem is used to derive the proposed technique. >

In the past, several heuristic algorithms were developed for the topological via minimization problem. It was very recently shown to be NP-hard even for the two-layer channel routing case with two-terminal nets only. The authors show that if no local net exists in a channel, this problem is solvable in O(kn/sup 2/) time even for k layers, where n is the number of two-terminal nets. As an extension of this case, they consider the problem for the case of k-layer circular channel routing in which no local net exists and present an O(n/sup 2k+1/) time algorithm. >

It is well known that some stochastic systems (e.g., semiMarkov systems) can be modeled by signal flow graphs. For such systems time-domain, transform, and simulation methods are available for analysis. The time-domain method has not been popular because of the requirement for numerous convolutions and deconvolutions, which are very timeconsuming and subject to error propagation. In this paper a method of minimizing the number of multiplications required to evaluate the symbolic gain expression for an acyclic signal flow graph is presented. For stochastic systems these multiplications correspond to time-domain convolutions. The method requires an N! search, where N is the number of internal nodes of the signal flow graph. To avoid this N! search a heuristic algorithm is implemented in a computer program (Symbolic Analysis-Minimal Multiplications (SAMM)) and examples of its application to semi-Markov systems are discussed.

The authors discuss network flow concepts as a means of modeling a large multiriver system with cascaded hydro plants for purposes of generation scheduling. The reservoir dynamics are described by network flow balance equations. A nonlinear modeling approach is taken to represent hydro-plant generating characteristics, and variable reservoir heads are permitted. The system model recognizes security constraints in the form of interregional transmission-capacity limitations. The resulting large-scale mathematical programming problem is solved by using a reduced-gradient algorithm specialized to exploit the embedded network structure of the hydrological system. The additional security constraints are handled by a gradient-protection scheme that is based on estimates of the Lagrange multipliers associated with binding constraints. The estimates of the multipliers are determined by solving a small, quadratic minimization problem. >

The fast Kalman algorithms are stabilized by introducing a quantity that measures the accumulation of the roundoff errors. This quantity is used to correct the variables of the algorithm at every time step. The correction is defined as the solution of a specific minimization problem. The resulting algorithm still has the nice complexity properties of the original algorithm (linear in the number of parameters to be estimated), but it has a much more stable behavior. >

In this note we discuss the H^{\infty} -sensitivity minimization problem for linear time-invariant delay systems. While the unweighted case reduces to simple Nevanlinna-Pick interpolation, the weighted case turns out to be much more complicated and demands certain functional-analytic techniques for its solution.

This paper presents a new optimal-design-oriented stability condition for 2-D state-space digital filters. A general formulation for optimal design of 2-D recursive digital filters is obtained by applying the new condition. The formulation can be reduced into an unconstrained minimization problem and be used to design 2-D state-space digital filters with an arbitrary response. Furthermore, the resulting filters are guaranteed to be not only stable but also able to suppress overflow oscillations due to adder overflows. Some practical design techniques for the spatialdomain specifications and the frequency-domain specifications are proposed on the basis of the general formulation. Several examples are given to show the effectiveness of the proposed techniques.

Based on graph theory, a study of via minimization problem is presented. We show that the simplest problem of this type is NP-complete and propose a heuristic algorithm for topological via minimization.

The Walsh-Hadamard transform (WHT) provides a one-to-one mapping of n-variable Boolean functions onto an n-dimensional transform space. As such, it enables synthesis procedures to be carried out in the transform domain. This short paper discusses the role of the WHT in extracting prime implicants, which is pertinent to the overall minimization problem. First, a procedure to identify all the prime implicants of a 1-vertexl located at the origin is developed by inspecting the elements of a single inverse transform. Second, a theorem is proved to show how the signs of the transform coefficients can be changed, to obtain all the prime implicants of an arbitrazy 1-vertex via the same inverse transforn operation.

A method for the design of time-limited and effectively band-limited waveforms for analog communication systems is developed. The design problem is first formulated in the L_2 (0, T) space. Nonlinear modulation threshold effects are incorporated directly into the design by introducing constraints in the form of minimum distance between points on the locus. It is shown that all pertinent information can be expressed in terms of the inner product function generated by the locus and its cross derivative. The design is then transformed into a constrained minimization problem in a space of inner product functions. The cases of stationary locus and N -dimensional locus are further investigated.

A procedure is illustrated to reduce the number of classes of internal states to be considered in the state minimization problem for incompletely specified sequential machines. The procedure leads to an extension of the definition of prime compatibility classes of states. It is based on the updating of the logical closure constraints for prime classes due to previous eliminations of nonprime ones. An additional, more complex elimination mechanism is also presented.

The solution of the l/sub 1/ sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better-known H infinity sensitivity minimization problem or the LQG (linear quadratic Gaussian) problem is given of a one-parameter family of first-order plants where the order of the l/sub 1/-optimal compensator can be arbitrarily large, and thus it is impossible to bound the order of an l/sub 1/-optimal compensator in terms of the order of the plant. A plant is considered which has a continuous one-parameter family of l/sub 1/-optimal compensators, and thus l/sub 1/-optimal compensators need not be unique. The author's two examples are considered to answer two questions left open by M.A. Daleh and J.B. Pearson (ibid., vol.32, p.314-23, 1987). >