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This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem à la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback–Leibler pseudo-distance, which gives rise to a convex optimization problem. After developing the variational analysis, we discuss the properties of an efficient algorithm for the solution of the corresponding dual problem, based on the iteration of a nonlinear map in a bounded subset of the dual space. Our main result is the proof of local convergence of the latter, established as a consequence of the central manifold theorem. Supported by numerical evidence, we conjecture that, in the mentioned bounded set, the convergence is actually global. [ABSTRACT FROM AUTHOR]

This paper presents a constructive method for (sub)optimal finite-impulse response (FIR) approximation of infinite-impulse response (IIR) models. The method minimizes the Hankel norm of the approximation error by using an explicit solution to the norm-preserved dilation problem. It has advantages over the existing methods in that it is a unified method for both single-input single-output and multiple-input multiple-output systems which allows direct tradeoff between .the least-squares and Chebyshev error criteria by using a single tuning parameter, and that the approximation algorithm is constructive and only involves algebraic manipulations rather than iteration and convex optimization procedures. The lower and upper bounds on the l² and Chebyshev norms of the approximation error are derived and are related to the tuning parameter. The problem of approximating noncausal IIR models by causal FIR models is also formulated and solved. The effectiveness and properties of the proposed algorithms are demonstrated by examples. [ABSTRACT FROM AUTHOR]

This paper describes an efficient algorithm for designing lattice wave digital (LWD) filters (parallel connections of two all-pass filters) with short-coefficient wordlength. The coefficient optimization is performed using the following three steps. First, an initial infinite-precision filter is designed such that it exceeds the given criteria in order to provide some tolerance for co-efficient quantization. Second, a nonlinear optimization algorithm is used for determining a parameter space of the infinite-precision coefficients including the feasible space where the filter meets the given criteria. The third step involves finding the filter parameters in this space so that the resulting filter meets the given criteria with the simplest coefficient representation forms. The proposed algorithm guarantees that the optimum finite-precision solution can be found for both the fixed-point binary and multiplierless coefficient representation forms. In addition, this algorithm is applicable for producing the desired finite-precision solutions for both conventional and approximately linear-phase LWD filters. Comparisons with some other existing quantization schemes show that the proposed algorithm gives the best finite-precision solutions in all examples taken from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study a matricial version of a generalized moment problem with degree constraint. We introduce a new metric on multivariable spectral densities induced by the family of their spectral factors, which, in the scalar case, reduces to the Hellinger distance. We solve the corresponding constrained optimization problem via duality theory. A highly nontrivial existence theorem for the dual problem is established in the Byrnes-Lindquist spirit. A matricial Newton-type algorithm is finally provided for the numerical solution of the dual problem. Simulation indicates that the algorithm performs effectively and reliably. [ABSTRACT FROM AUTHOR]

Consider an agent who seeks to traverse the shortest path in a graph having random edge weights. If the agent has no side information about the realizations of the edge weights, it should simply take the path of least average length. We consider a generalization of this framework whereby the agent has access to a limited amount of side information about the edge weights ahead of choosing a path. We define a measure for information quantity, provide bounds on the agent's performance relative to the amount of side information it receives, and present algorithms for optimizing side information. The results are based on a new graph characterization tied to shortest path optimization. [ABSTRACT FROM AUTHOR]

We consider the problem of monitoring spatial phenomena, such as road speeds on a highway, using wireless sensors with limited battery life. A central question is to decide where to locate these sensors to best predict the phenomenon at the unsensed locations. However, given the power constraints, we also need to determine when to activate these sensors in order to maximize the performance while satisfying lifetime requirements. Traditionally, these two problems of sensor placement and scheduling have been considered separately; one first decides where to place the sensors, and then when to activate them. [ABSTRACT FROM AUTHOR]

We examine the theoretical and numerical global convergence properties of a certain "gradient free" stochastic approximation algorithm called the "simultaneous perturbation stochastic approximation (SPSA)" that has performed well in complex optimization problems. We establish two theorems on the global convergence of SPSA, the first involving the well-known method of injected noise. The second theorem establishes conditions under which "basic" SPSA without injected noise can achieve convergence in probability to a global optimum, a result with important practical benefits. [ABSTRACT FROM AUTHOR]