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In this paper, we consider near-optimal operation for a class of unconstrained batch processes using the self-optimizing control (SOC) methodology. The existing static SOC approach is extended to the dynamic case by means of a static reformulation of the dynamic optimization problem. However, the dynamic SOC problem is posed as a structure-constrained controlled variable (CV) selection problem, which is different from the static cases. A lower-block triangular structure is specified for the combination matrix, H , to allow for optimal operation whilst respecting causality. A new result is that the structure-constrained SOC problem still results in a convex formulation, which has an analytic solution where the optimal CVs associated with discrete time instants are solved separately. In addition, the inputs are directly determined based on current CV functions for on-line utilization. A fed-batch reactor and a batch distillation column are used to demonstrate the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, new classes of nondifferentiable functions constituting multiobjective programming problems are introduced. Namely, the classes of --type I objective and constraint functions and, moreover, the various classes of generalized --type I objective and constraint functions are defined for directionally differentiable multiobjective programming problems. Sufficient optimality conditions and various Mond–Weir duality results are proved for nondifferentiable multiobjective programming problems involving functions of such type. Finally, it is showed that the introduced --type I notion with is not a sufficient condition for Wolfe weak duality to hold. These results are illustrated in the paper by suitable examples. [Copyright &y& Elsevier]

Abstract: The focus of this paper is the optimization of complex multi-parameter systems. We consider systems in which the objective function is not known explicitly, and can only be evaluated through computationally intensive numerical simulation or through costly physical experiments. The objective function may also contain many local extrema which may be of interest. Given objective function values at a scattered set of parameter values, we develop a response surface model that can dramatically reduce the required computation time for parameter optimization runs. The response surface model is developed using radial basis functions, producing a model whose objective function values match those of the original system at all sampled data points. Interpolation to any other point is easily accomplished and generates a model which represents the system over the entire parameter space. This paper presents the details of the use of radial basis functions to transform scattered data points, obtained from a complex continuum mechanics simulation of explosive materials, into a response surface model of a function over the given parameter space. Response surface methodology and radial basis functions are discussed in general and are applied to a global optimization problem for an explosive oil well penetrator. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to establish that there exist suitable objective functions for mathematical programming formulations of dynamic user equilibrium assignment in the sense of . Recently, showed that we cannot necessarily calculate a dynamic user equilibrium assignment by minimising the integral over time of Beckmann’s objective function that is widely used to solve for static user equilibrium assignment. In the present paper, two distinct objective functions are presented that result from formulations of assignment either as a variational inequality or as an infinitesimal optimisation: each of these formulations can be solved as a forward dynamic programme. With these formulations and solution approaches, we solve an example based upon Lin and Lo’s one correctly. [Copyright &y& Elsevier]

In this paper, we consider damping optimization in mechanical system excited by an external force. We use optimization criteria based on minimizing average energy amplitude and average displacement amplitude over the arbitrary time. As the main result we derive explicit formulas for objective functions. These formulas can be implemented efficiently and accelerate optimization process significantly, which is illustrated in a numerical example. [ABSTRACT FROM AUTHOR]

Linear Discriminant Analysis (LDA) is a standard tool for classification and dimension reduction in many applications. However, the problem of high dimension is still a great challenge for the classical LDA. In this paper we consider the supervised pattern classification in the high dimensional setting, in which the number of features is much larger than the number of observations and present a novel approach to the sparse optimal scoring problem using the zero-norm. The difficulty in treating the zero-norm is overcome by using appropriate continuous approximations such that the resulting problems are solved by alternating schemes based on DC (Difference of Convex functions) programming and DCA (DC Algorithms). The experimental results on both simulated and real datasets show the efficiency of the proposed algorithms compared to the five state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper studies the problem of adaptive neural output feedback controller design for a class of uncertain switched stochastic nonlinear systems in strict-feedback form. In the design procedure, a common coordinate transformation for all subsystems is constructed to overcome the design difficulty caused by adoption of different coordinate transformation for different subsystems. Then, by using switched state observer to estimate the unmeasured states and different update laws for different subsystems, a novel neural output-feedback controller is designed via backstepping approach. Furthermore, based on the Lyapunov method and the average dwell time condition, the stability of the resulting closed-loop system can be achieved. It is shown that all the signals of the closed-loop system are bounded under a class of switching signals with average dwell time. Finally, simulation results are included for validating the advantages of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problems of finite-time filter analysis and design for discrete time-delay neural networks with Markovian jump parameters and sector-bounded activation functions represented by Takagi–Sugeno fuzzy model. Firstly, a sufficient admissibility criterion is presented to guarantee that the augmented fuzzy jump neural network without parameter uncertainties is stochastically finite-time bounded in a prescribed time interval. From the admissibility criterion obtained, a sufficient condition on stochastic finite-time boundedness is provided for the augmented fuzzy jump neural networks. Then, a sufficient criterion to design a finite-time fuzzy filter is presented with uncertain parameters and Markovian jumps for discrete time-delay fuzzy neural networks. Moreover, conditions on stochastic finite-time stability are also established for nominal and uncertain delayed fuzzy jump neural networks without the presence of external disturbance. All criteria obtained can be represented as the form of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper proposes a novel region-based active contour model in the level set formulation for medical image segmentation. We define a unified fitting energy framework based on Gaussian probability distributions to obtain the maximum a posteriori probability (MAP) estimation. The energy term consists of a global energy term to characterize the fitting of global Gaussian distribution according to the intensities inside and outside the evolving curve, as well as a local energy term to characterize the fitting of local Gaussian distribution based on the local intensity information. In the resulting contour evolution that minimizes the associated energy, the global energy term accelerates the evolution of the evolving curve far away from the objects, while the local energy term guides the evolving curve near the objects to stop on the boundaries. In addition, a weighting function between the local energy term and the global energy term is proposed by using the local and global variances information, which enables the model to select the weights adaptively in segmenting images with intensity inhomogeneity. Extensive experiments on both synthetic and real medical images are provided to evaluate our method, show significant improvements on both efficiency and accuracy, as compared with the popular methods. [ABSTRACT FROM AUTHOR]

Abstract: Recently, Gandomi and Alavi proposed a meta-heuristic optimization algorithm, called Krill Herd (KH), for global optimization [Gandomi AH, Alavi AH. Krill Herd: A New Bio-Inspired Optimization Algorithm. Communications in Nonlinear Science and Numerical Simulation, 17(12), 4831–4845, 2012.]. This paper represents an optimization method to global optimization using a novel variant of KH. This method is called the Stud Krill Herd (SKH). Similar to genetic reproduction mechanisms added to KH method, an updated genetic reproduction schemes, called stud selection and crossover (SSC) operator, is introduced into the KH during the krill updating process dealing with numerical optimization problems. The introduced SSC operator is originated from original Stud genetic algorithm. In SSC operator, the best krill, the Stud, provides its optimal information for all the other individuals in the population using general genetic operators instead of stochastic selection. This approach appears to be well capable of solving various functions. Several problems are used to test the SKH method. In addition, the influence of the different crossover types on convergence and performance is carefully studied. Experimental results indicate an instructive addition to the portfolio of swarm intelligence techniques. [Copyright &y& Elsevier]

Abstract: In this paper, using the remote start or dissipative method, we investigate ergodicity for several kinds of functional stochastic equations including functional stochastic differential equations (SDEs) with variable delays, neutral functional SDEs, functional SDEs driven by jump processes, and semi-linear functional stochastic partial differential equations (SPDEs). Using the ergodicity derived, we then treat a couple of applications in stochastic approximation and optimization problems. [Copyright &y& Elsevier]

Abstract: In modern finite element analysis (FEA), a mesh is said to be ‘tangled’ if it contains one or more inverted elements. Tangling can occur, for example, during mesh optimization and mesh morphing. Modern finite element theory and commercial FEA packages are not designed to handle tangled meshes, i.e., they can lead to erroneous results. Researchers and practitioners therefore unanimously recommend untangling prior to analysis. In this paper, a new mathematical framework for FEA over tangled meshes is proposed. Specifically, by defining a cell decomposition of a tangled mesh, and an associated set of cell shape functions, it is shown that FEA can be successfully carried out over tangled meshes. The cell shape functions are constructed through an oriented linear combination of the classic element shape functions. Numerical examples illustrate the correctness of the proposed framework. Potential applications of the proposed framework are also illustrated. [Copyright &y& Elsevier]

Abstract: This paper deals with set-valued vector optimization problems and set-valued vector variational inequalities in topological vector spaces, and provides some scalarization approaches for these problems by means of the polar cone and Gerstewitz’s scalarization functions. [Copyright &y& Elsevier]

Abstract: Systems of nonlinear equations are ubiquitous in engineering, physics and mechanics, and have myriad applications. Generally, they are very difficult to solve. In this paper, we will present a filled function method to solve nonlinear systems. We will first convert the nonlinear systems into equivalent global optimization problems with the property: is a global minimizer if and only if its function value is zero. A filled function method is proposed to solve the converted global optimization problem. Numerical examples are presented to illustrate our new techniques. [Copyright &y& Elsevier]

Abstract: In this paper, we consider (weak) vector variational-like inequality problems ((W)VLIP) and (weak) vector optimization problems ((W)VOP), and check their relationships through the existence of solutions in topological vector spaces. [Copyright &y& Elsevier]

Abstract: We consider a class of global optimization problems, in which the objective function is Lebesgue integrable. In this paper, we present a sufficient and necessary condition for computing the essential infimum. This optimality condition can be used to design algorithms for solving the global optimization problem. [Copyright &y& Elsevier]

Abstract: In this paper, a new filled function which has better properties is proposed for identifying a global minimum point for a general class of nonlinear programming problems within a closed bounded domain. An algorithm for unconstrained global optimization is developed from the new filled function. Theoretical and numerical properties of the proposed filled function are investigated. The implementation of the algorithm on seven test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]

Abstract: In this paper, by introducing a new nonmonotone line search technique and combining it with the spectral projected gradient method, we propose a solution method for solving the bound constrained optimization problems. Under mild conditions, we obtain the global convergence even without requiring a prior of the existence of a limit point. Numerical tests are also given to show the efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: Some constrained optimization approaches have been recently proposed for the system of nonlinear equations (SNE). Filter approach with line search technique is employed to attack the system of nonlinear equations in this paper. The system of nonlinear equations is transformed into a constrained nonlinear programming problem at each step, which is then solved by line search strategy. Furthermore, at each step, some equations are treated as constraints while the others act as objective functions, and filter strategy is then utilized. In essence, constrained optimization methods combined with filter technique are utilized to cope with the system of nonlinear equations. [Copyright &y& Elsevier]

This paper is a study of the complexity of optimization of continuous univariate functions using a fixed number of sequentially selected function evaluations. The complexity is studied in the average case under a conditioned Wiener measure. We show that to obtain an error of at most , on the order of function evaluations are required. [Copyright &y& Elsevier]

Abstract: This paper deals with characterizations of strictly semi-monotone (semi-monotone) properties in nonsmooth functions that are H-differentiable. These results give a unified treatment of such results for C 1-functions, semi-smooth functions, and for locally Lipschitzian functions. Illustrations to nonlinear complementarity problems are given to show the usefulness of our results. [Copyright &y& Elsevier]

Abstract: Seeking global optima of an unconstrained and multi-modal global optimization problem by constructing a filled function is concerned in this paper. On the basis of analyzing filled functions presented before, a new filled function is proposed, and it is proved to meet the properties of a filled function. Moreover, solutions of numerical experiments show that the function is quite effective. [Copyright &y& Elsevier]

Abstract: This paper concerns the step-size estimation in line search method for unconstrained optimization problems. Some new approaches for estimating the step size are proposed and the global convergence of related line search methods are analyzed. Finally, we discuss the choice of the initial step size in Armijo line search rule. [Copyright &y& Elsevier]

Abstract: Almost all the existing continuous neural networks now for associative memory are based on optimizing a quadratic function. The disadvantage is that the structure is complicated and implementation of circuit cannot coincide with the theoretical analysis. In this paper, a new linear neural network is presented for associative memory. Simple in nature, the proposed network is proved to be an ideal associative memory. Compared with other networks, the main difference is that each pattern to be recognized is used as a parameter of the network other than an initial point. The main advantage is that the theoretic analysis coincides precisely with the easy implementation and the network can explain clearly the meaning of each refused pattern. The model considered herein is intrinsically a neural network for solving linear optimization problems with hybrid constraints. But its state is allowed to lie in a general closed convex set spanned by the prototype patterns. The performance of the proposed network is demonstrated by means of simulation of one numerical example. [Copyright &y& Elsevier]

Abstract: In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported. [Copyright &y& Elsevier]

Line search methods are traditional and successful methods for solving unconstrained optimization problems. Its convergence has attracted more attention in recent years. In this paper we analyze the general results on convergence of line search methods with seven line search rules. It is clarified that the search direction plays a main role in these methods and that step-size guarantees the global convergence in some cases. It is also proved that many line search methods have same convergence property. These convergence results can enable us to design powerful, effective, and stable algorithms in practice. Finally, a class of special line search methods is investigated. [Copyright &y& Elsevier]

This paper presents an interval optimization method to solve the uncertain problems of the vibration systems with multi-degrees of freedom, where the structural characteristics are assumed to be expressed as interval parameters. Combining the interval extension of function with the first-order Taylor expansions of the functions, the interval optimization method is derived. The present method is implemented for a torsional vibration system and a frame structure. The numerical results show that the method is effective, and that the present method can provide more information about the optimization results than those obtained by the deterministic optimization. [Copyright &y& Elsevier]