derivative-free optimization – Page 7

BFO, a trainable derivative-free Brute Force Optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables

Published: 2015/07/03, Updated: 2017/07/13

(Mixed) Integer Nonlinear Programming, Bound-constrained Optimization, Nonlinear Optimization bound constraints, derivative-free optimization, direct search, mixed-integer programming, trainable algorithms

A direct-search derivative-free Matlab optimizer for bound-constrained problems is described, whose remarkable features are its ability to handle a mix of continuous and discrete variables, a versatile interface as well as a novel self-training option. Its performance compares favourably with that of NOMAD, a state-of-the art package. It is also applicable to multilevel equilibrium- or … Read more

A second-order globally convergent direct-search method and its worst-case complexity

Published: 2015/06/04

Serge Gratton

Clément W. Royer

Luis Nunes Vicente

Nonlinear Optimization, Unconstrained Optimization derivative-free optimization, direct search, second-order, worst-case complexity

Direct-search algorithms form one of the main classes of algorithms for smooth unconstrained derivative-free optimization, due to their simplicity and their well-established convergence results. They proceed by iteratively looking for improvement along some vectors or directions. In the presence of smoothness, first-order global convergence comes from the ability of the vectors to approximate the steepest … Read more

Stochastic Optimization using a Trust-Region Method and Random Models

Published: 2015/04/15

Ruobing Chen

Matt Menickelly

Katya Scheinberg

Stochastic Programming, Unconstrained Optimization derivative-free optimization, probabilistic models, stochastic optimization, trust-region methods

In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic observations of the function or its gradient. Our method also utilizes estimates of function values to gauge progress that is being made. The convergence analysis … Read more

A trust-funnel method for nonlinear optimization problems with general nonlinear constraints and its application to derivative-free optimization

Published: 2015/01/26

Phillipe Sampaio

Philippe L. Toint

Constrained Nonlinear Optimization constrained nonlinear optimization, derivative-free optimization, trust funnel, trust-region methods

A trust-funnel method is proposed for solving nonlinear optimization problems with general nonlinear constraints. It extends the one presented by Gould and Toint (Math. Prog., 122(1):155-196, 2010), originally proposed for equality-constrained optimization problems only, to problems with both equality and inequality constraints and where simple bounds are also considered. As the original one, our method … Read more

Trust-region methods without using derivatives: Worst case complexity and the non-smooth case

Published: 2015/01/26

R. Garmanjani

Luis Nunes Vicente

Diogo Júdice

Nonsmooth Optimization, Unconstrained Optimization composite functions, derivative-free optimization, non-smoothness, smoothing, trust-region methods, worst-case complexity

Trust-region methods are a broad class of methods for continuous optimization that found application in a variety of problems and contexts. In particular, they have been studied and applied for problems without using derivatives. The analysis of trust-region derivative-free methods has focused on global convergence, and they have been proved to generate a sequence of … Read more

Use of a Biobjective Direct Search Algorithm in the Process Design of Material Science Applications

Published: 2014/12/02, Updated: 2015/08/03

Chemical Engineering, Nonlinear Optimization alloys design, biobjective optimization, blackbox optimization, derivative-free optimization, material science, mesh adaptive direct search, process design

This work describes the application of a direct search method to the optimization of problems of real industrial interest, namely three new material science applications designed with the FactSage software. The search method is BiMADS, the biobjective version of the mesh adaptive direct search (MADS) algorithm, designed for blackbox optimization. We give a general description … Read more

Linear equalities in blackbox optimization

Published: 2014/05/28, Updated: 2015/03/31

Charles Audet

Sébastien Le Digabel

Mathilde Peyrega

Constrained Nonlinear Optimization blackbox optimization, convergence analysis, derivative-free optimization, linear equality constraints, mads

The Mesh Adaptive Direct Search (Mads) algorithm is designed for blackbox optimization problems subject to general inequality constraints. Currently, Mads does not support equalities, neither in theory nor in practice. The present work proposes extensions to treat problems with linear equalities whose expression is known. The main idea consists in reformulating the optimization problem into … Read more

Dynamic scaling in the Mesh Adaptive Direct Search algorithm for blackbox optimization

Published: 2014/03/31

Charles Audet

Sébastien Le Digabel

Christophe Tribes

Constrained Nonlinear Optimization, Nonsmooth Optimization blackbox optimization, derivative-free optimization, dynamic scaling, mesh adaptive direct search

Blackbox optimization deals with situations in which the objective function and constraints are typically computed by launching a time-consuming computer sim- ulation. The subject of this work is the Mesh Adaptive Direct Search (MADS) class of algorithms for blackbox optimization. We propose a way to dynamically scale the mesh, which is the discrete spatial structure … Read more

Direct search based on probabilistic descent

Published: 2014/03/19

Convex and Nonsmooth Optimization, Nonlinear Optimization, Stochastic Programming derivative-free optimization, direct search, polling, positive spanning sets, probabilistic descent, random directions

Direct-search methods are a class of popular derivative-free algorithms characterized by evaluating the objective function using a step size and a number of (polling) directions. When applied to the minimization of smooth functions, the polling directions are typically taken from positive spanning sets which in turn must have at least n+1 vectors in an n-dimensional … Read more

A globally convergent trust-region algorithm for unconstrained derivative-free optimization

Published: 2014/03/10, Updated: 2022/05/13

Priscila Savulski Ferreira

Elizabeth Wegner Karas

Mael Sachine

Nonlinear Optimization, Other Topics, Unconstrained Optimization derivative-free optimization, polynomial interpolation and global convergence, trust-region methods, unconstrained optimization

In this work we explicit a derivative-free trust-region algorithm for unconstrained optimization based on the paper (Computational Optimization and Applications 53: 527-555, 2012) proposed by Powell. The objective function is approximated by quadratic models obtained by polynomial interpolation. The number of points of the interpolation set is fixed. In each iteration only one interpolation point … Read more