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This monograph is a state-of-the-art presentation of algorithms for solving a class of optimization problems that are benign in the sense that their objective functions are reasonably smooth, unconstrained, and defined over a relatively small number of variables (say up to a hundred). However, the problems are extremely challenging from an algorithmic… (More)

- Andrew R. Conn, Katya Scheinberg, Luís N. Vicente
- SIAM Journal on Optimization
- 2009

In this paper we prove global convergence for first and second-order stationary points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of quadratic (or linear) models built from evaluating the objective function at sample sets. The derivative-free models are required… (More)

- A. Ismael F. Vaz, Luís N. Vicente
- J. Global Optimization
- 2007

In this paper we develop, analyze, and test a new algorithm for the global minimization of a function subject to simple bounds without the use of derivatives. The underlying algorithm is a pattern search method, more specifically a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the optional… (More)

- Paul H. Calamai, Luís N. Vicente
- ACM Trans. Math. Softw.
- 1994

This paper describes a technique for generating sparse or dense quadratic bilevel programming problems with a selectable number of known global and local solutions. The technique described here does not require the solution of any subproblems. In addition, since most techniques for solving these problems begin by solving the corresponding relaxed quadratic… (More)

- Luís N. Vicente, Paul H. Calamai
- J. Global Optimization
- 1994

- Andrew R. Conn, Katya Scheinberg, Luís N. Vicente
- Math. Program.
- 2008

We consider derivative free methods based on sampling approaches for nonlinear optimization problems where derivatives of the objective function are not available and cannot be directly approximated. We show how the bounds on the error between an interpolating polynomial and the true function can be used in the convergence theory of derivative free sampling… (More)

- A. L. Custódio, J. F. Aguilar Madeira, A. Ismael F. Vaz, Luís N. Vicente
- SIAM Journal on Optimization
- 2011

In practical applications of optimization it is common to have several conflicting objective functions to optimize. Frequently, these functions are subject to noise or can be of black-box type, preventing the use of derivative-based techniques. We propose a novel multiobjective derivative-free methodology, calling it direct multisearch (DMS), which does not… (More)

- A. L. Custódio, Luís N. Vicente
- SIAM Journal on Optimization
- 2007

Pattern search methods can be made more efficient if past function evaluations are appropriately reused. In this paper we will introduce a number of ways of reusing previous evaluations of the objective function based on the computation of simplex derivatives (e.g., simplex gradients) to improve the efficiency of a pattern search iteration. At each… (More)

- A. L. Custódio, Humberto Rocha, Luís N. Vicente
- Comp. Opt. and Appl.
- 2010

The goal of this paper is to show that the use of minimum Frobenius norm quadratic models can improve the performance of direct-search methods. The approach taken here is to maintain the structure of directional direct-search methods, organized around a search and a poll step, and to use the set of previously evaluated points generated during a… (More)

- Matthias Heinkenschloss, Luís N. Vicente
- SIAM Journal on Optimization
- 2002

In this paper we study the global convergence behavior of a class of composite–step trust–region SQP methods that allow inexact problem information. The inexact problem information can result from iterative linear systems solves within the trust–region SQP method or from approximations of first–order derivatives. Accuracy requirements in our trust– region… (More)