Abstract. Inspired by a method by Jones et al. (1993), we present a global optimization algorithm based on multilevel coordinate search. It is guaranteed to converge if the function is continuous in the neighborhood of a global minimizer. By starting a local search from certain good points, an improved convergence result is obtained. We discuss implementation details and give some numerical results.

We present a new and fast method, called the cross-entropy method, for finding the optimal solution of combinatorial and continuous nonconvex optimization problems with convex bounded domains. To find the optimal solution we solve a sequence of simple auxiliary smooth optimization problems based on Kullback-Leibler cross-entropy, importance sampling, Markov chain and Boltzmann distribution. We use importance sampling as an important ingredient for adaptive adjustment of the temperature in the Boltzmann distribution and use Kullback-Leibler cross-entropy to find the optimal solution. In fact, we use the mode of a unimodal importance sampling distribution, like the mode of beta distribution, as an estimate of the optimal solution for continuous optimization and Markov chains approach for combinatorial optimization. In the later case we show almost surely convergence of our algorithm to the optimal solution. Supporting numerical results for both continuous and combinatorial optimization problems are given as well. Our empirical studies suggest that the crossentropy method has polynomial in the size of the problem running time complexity.

Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables.

A benchmarking suite describing over 1000 optimization problems and constraint satisfaction problems covering problems from dierent traditions is described, annotated with best known solutions, and accompanied by recommended benchmarking protocols for comparing test results.

Constrained optimization has been extensively used to... This paper briefly reviews some methods available to solve these problems and describes a new suite of tools for working with MPEC models. Computational results demonstrating...

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. This paper presents an overview of the deterministic global optimization approaches and their applications in the areas of Process Design, Control, and Computational Chemistry. The focus is on (i) decomposition-based primal dual methods, (ii) methods for generalized geometric programming problems, and (iii) global optimization methods for general nonlinear programming problems. The classes of mathematical problems that are addressed range from indefinite quadratic programming to concave programs, to quadratically constrained problems, to polynomials, to general twice continuously differentiable nonlinear optimization problems. For the majority of the presented methods nondistributed global optimization approaches are discussed with the exception of decomposition-based methods where a distributed global optimization approach is presented. 1. Background. A significant effort has been expended in the last five decades toward theoretical and algorithmic studies of applications that arise...

We demonstrate how the separable least-squares technique of Golub and Pereyra can be exploited in the identification of both linear and non-linear systems based on the prediction error formulation. The model classes to be considered here are the output error model and innovations model in the linear case and the Wiener system in the non-linear case. This technique together with a suitable choice of parameterization allow us to solve, in the linear case, the associated optimization problem using only np parameters instead of the usual n#m + p#+mp parameters when canonical forms are used, where n, m and p denote respectively the number of states, inputs and outputs. We also prove under certain assumptions that the separable optimization method is numerically better conditioned than its non-separable counterpart. Successful operations of these identi#cation algorithms are demonstrated by applying them to two sets of industrial data: an industrial dryer in the linear case and a high purity ...

The paper considers the intensity modulated radiation therapy (inverse) treatment planning. An approach to determine the trajectories of the leaves of the multileaf collimator (MLC) in order to produce the prescribed intensity distribution is developed. The paper concentrates on the multiple static delivery technique. A mathematical model for calculating the intensity distribution with the help of locations of the leafheads of subsequent subfields is constructed. Furthermore an optimization model in which the decision variables are the locations of leafheads is developed. The relevant constraints are considered as well. The optimization problem is a large dimensional constrained nonlinear global extremum problem. It is solved by the LGO (Lipschitz (Continuous) Global Optimizer) program system. Comparisons with other optimization method (Hooke-Jeeves iteration) are included. Numerical experiments are presented to confirm the functionality of the method. AMS-classification: 49-...

We propose a general scheme of reduction of a Lipschitz programming problem to a problem of minimizing increasing convex-along-rays function. It is based on the positively homogeneous extension of degree p of the objective function and projective transformation of IR n + onto the unit simplex. The application of cutting angle method to Lipschitz programming is considered. Keywords: Lipschitz programming, abstract convexity, cutting angle method 1 Introduction During the recent years a great attention has been drawn to problems of global optimization of non-convex functions. One of the most important classes of such functions are Lipschitz functions. A number of algorithms for their minimization were proposed, typically methods of branch and bound type or random search methods (see [18] for detailed discussion of the topic and also [11, 23]). The known methods have led to solution of certain problems with hundreds of variables, but their efficiency depends on the particular structure...