derivative-free optimization – Page 8

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

Published: 2015/01/26

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

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

A derivative-free trust-funnel method for equality-constrained nonlinear optimization

Published: 2014/02/27

Phillipe Sampaio

Philippe L. Toint

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

In this work, we look into new derivative-free methods to solve equality-constrained optimization problems. Of particular interest, are the trust-region techniques, which have been investigated for the unconstrained and bound-constrained cases. For solving equality-constrained optimization problems, we introduce a derivative-free adaptation of the trust-funnel method combined with a self-correcting geometry scheme and present some encouraging … Read more

A Linesearch-based Derivative-free Approach for Nonsmooth Optimization

Published: 2013/05/13, Updated: 2015/03/15

Constrained Nonlinear Optimization derivative-free optimization, exact penalty functions, inequality constrained optimization, lipschitz optimization, stationarity conditions

In this paper, we propose new linesearch-based methods for nonsmooth optimization problems when first-order information on the problem functions is not available. In the first part, we describe a general framework for bound-constrained problems and analyze its convergence towards stationary points, using the Clarke-Jahn directional derivative. In the second part, we consider inequality constrained optimization … Read more

Convergence of trust-region methods based on probabilistic models

Published: 2013/04/23, Updated: 2013/10/25

A. S. Bandeira

Katya Scheinberg

Luis Nunes Vicente

Nonlinear Optimization, Stochastic Programming derivative-free optimization, global convergence, probabilistic models, trust-region methods, unconstrained optimization

In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions. Our method and setting differs from many stochastic optimization approaches in two principal ways. Firstly, we assume that the value of the function itself can be computed without noise, in … Read more

Worst case complexity of direct search under convexity

Published: 2013/04/23

M. Dodangeh

Luis Nunes Vicente

Convex and Nonsmooth Optimization, Nonlinear Optimization convexity, derivative-free optimization, direct search, sufficient decrease, worst-case complexity

In this paper we prove that the broad class of direct-search methods of directional type, based on imposing sufficient decrease to accept new iterates, exhibits the same global rate or worst case complexity bound of the gradient method for the unconstrained minimization of a convex and smooth function. More precisely, it will be shown that … Read more