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.

. In this paper we propose a form of the DIRECT algorithm that is strongly biased toward local search. This form should do well for small problems with a single global minimizer and only a few local minimizers. We motivate our formulation with some results on how the original formulation of the DIRECT algorithm clusters its search near a global minimizer. We report on the performance of our algorithm on a suite of test problems and observe that the algorithm performs particularly well when termination is based on a budget of function evaluations. Key words. DIRECT, local clustering, local bias 1. Introduction. The DIRECT (DIviding RECTangles) algorithm [13, 14] is a pattern search method (in the sense of [17]) that balances local and global search in a attempt to efficiently find a global optimizer. Other deterministic sampling methods, such as implicit filtering [9, 15], MDS [6], Hooke-Jeeves [10], or Nelder-Mead [16], drive an approximate gradient to zero and are not designed for g...

The paper presents the toolbox NLPLIB TB 1.0 (NonLinear Programming LIBrary); a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares, box-bounded global optimization, global mixed-integer nonlinear programming, and exponential sum model fitting.

Many engineering optimization problems can be formulated as nonconvex nonlinear programming problems (NLPs) involving a nonlinear objective function subject to nonlinear constraints. Such problems may exhibit more than one locally optimal point. However, one is often solely or primarily interested in determining the globally optimal point. This thesis is concerned with techniques for establishing such global optima using spatial Branch-and-Bound (sBB) algorithms.

Abstract. This paper is concerned with the algorithmic behavior of the DIRECT (DIviding RECTangles) algorithm. We show that DIRECT is sensitive to additive scaling, and this sensitivity can affect convergence. We present a modified version of the algorithm, and illustrate the effectiveness of our modification with numerical results.

Levy and Montalvo, Yao, and Shima individually proposed tunneling algorithms. The tunneling algorithms employ analogy to tunnel effect in physics, and are used to optimize continuous systems. The present paper proposes a method of solving combinatorial problems using a type of randomized dynamic tunneling technique. This method is based on a computational model called CCM*. CCM* is an extended version of the Chemical Casting Model (CCM). CCM was proposed by the author toward developing a method of solving open and incompletely-specified problems that may change while being solved, using self-organizing computation. The 0--1 integer programming problem is solved using CCM* with a very simple rule and an evaluation function. CCM* allows us to escape from local maxima by composing the rule dynamically and randomly. This cannot be done by using the original production rule as is. Our experiments show that approximate solutions can be found more rapidly by CCM* than by using a branch-and-b...

der the direction of C.T. Kelley.) This work describes theoretical results, and practical improvements to the DIRECT Algorithm, a direct search global optimization algorithm for bound-constrained prob-lems. We rigorously show that a sub-sequence of the points sampled by the algorithm satisfy first order necessary conditions for both smooth and non-smooth problems. We show linear convergence of the algorithm for linear problems, and demonstrate why our analysis cannot be extended to more general problems. We analyze a parameter of DIRECT, and show that it negatively affects the per-formance of the algorithm. A modified version of the DIRECT is introduced. Test examples are used to demonstrate the effectiveness of the modified algorithm. We apply DIRECT to six well-field optimization problems from the literature. We collect data on the problems with DIRECT, and utilize statistical methods to glean information from the data about the well-field problems.

In this paper we will discuss the efficiency and implementation details of an algorithm for finding the global minimum of a multivariate function subject to simple bounds on the variables. The algorithm, DIRECT, developed by D. R. Jones, C. D. Perttunen and B. E. Stuckman is a modification of the standard Lipschitzian approach that eliminates the need to specify a Lipschitz constant. We have implemented the DIRECT algorithm in Matlab and the efficiency of our implementation is analyzed by comparing it to the result of Jones's implementation on nine standard test problems for global optimization. In fifteen out of eighteen runs the results is to the favor of our implementation. For some test problems the differences in the number of function evaluations needed for the algorithm to converge are small but for others the differences are great enough to be worth a discussion. Our code is integrated in the NLPLIB TB Toolbox as part of the optimization environment TOMLAB. All tests are perfor...

Abstract. In the paper, the global optimization problem of a multidimensional “black-box” function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this problem is presented. At each iteration of the method a number of possible Lipschitz constants is chosen from a set of values varying from zero to infinity. This idea is unified with an efficient diagonal partition strategy. A novel technique balancing usage of local and global information during partitioning is proposed. A new procedure for finding lower bounds of the objective function over hyperintervals is also considered. It is demonstrated by extensive numerical experiments performed on more than 1600 multidimensional test functions that the new algorithm shows a very promising performance. Key words. Global optimization, black-box functions, derivative-free methods, partition strategies, diagonal approach AMS subject classifications. 65K05, 90C26, 90C56 1. Introduction. Many

This paper proposes active handwriting models, in which kernel principal component analysis is applied to capture nonlinear handwriting variations. In the recognition phase, the chamfer distance transform and a dynamic tunnelling algorithm (DTA) are employed to search for the optimal shape parameters. The proposed methodology is successfully applied to a novel radical decomposition approach to the challenging problem of handwritten Chinese character recognition.