A pattern search and implicit filtering algorithm for solving linearly constrained minimization problems with noisy objective functions

PSIFA - Pattern Search and Implicit Filtering Algorithm - is a derivative-free algorithm that has been designed for linearly constrained problems with noise in the objective function. It combines some elements of the pattern search approach of Lewis and Torczon with ideas from the method of implicit filtering of Kelley enhanced with a further analysis of the current face and a simple extrapolation strategy for updating the step length. The feasible set is explored by PSIFA without any particular assumption about its description, being the equality constraints handled in their original formulation. Besides, compact bounds for the variables are not mandatory. The global convergence analysis is presented, encompassing the degenerate case, under mild assumptions. Numerical experiments with linearly constrained problems from the literature were performed. Additionally, problems with the feasible set defined by polyhedral 3D cones with several degrees of degeneration at the solution were addressed, including noisy functions that are not covered by the theoretical hypotheses. To put PSIFA in perspective, comparative tests have been prepared, with encouraging results344827852CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP302915/2016-82013/12964-4; 2013/05475-7; 2013/07375-

Derivative-free methods for nonlinear programming with general lowerlevel constraints

Abstract Augmented Lagrangian methods for derivative-free continuous optimization with constraints are introduced in this paper. The algorithms inherit the convergence results obtained by Andreani, Birgin, Martínez and Schuverdt for the case in which analytic derivatives exist and are available. In particular, feasible limit points satisfy KKT conditions under the Constant Positive Linear Dependence (CPLD) constraint qualification. The form of our main algorithm allows one to employ well established derivative-free sub-algorithms for solving lower-level constrained subproblems. Numerical experiments are presented

Nonmonotone Strategy for Minimization of Quadratics With Simple Constraints

An algorithm for quadratic minimization with simple bounds is introduced, combining, as many well-known methods do, active set strategies and projection steps. The novelty is that here the criterion for acceptance of a projected trial point is weaker than the usual ones, which are based on monotone decrease of the objective function. It is proved that convergence follows as in the monotone case. Numerical experiments with bound-constrained quadratic problems from CUTE collection show that the modified method is slightly more efficient, in practice, than its monotone counterpart and has a superior performance than the well-known code LANCELOT for this class of problems. Key words. Quadratic programming, conjugate gradients, active set methods. AMS subject classifications. 65K10, 49M07, 65F15, 90C20 1 Introduction The problem of minimizing a quadratic function f subject to bounds on the variables has many practical applications. Many times, physical and Institute of Mathematics, S..

Discrete Newton's method with local variations

A globally convergent discrete Newton method is proposed for solving large-scale nonlinear systems of equations. Advantage is taken from discretization steps so that the residual norm can be reduced while the Jacobian is approximated, besides the reduction at Newtonian iterations. The Curtis-Powell-Reid (CPR) scheme for discretization is used for dealing with sparse Jacobians. Global convergence is proved and numerical experiments are presented

CUTEr (and SifDec) a constrained and unconstrained testing environment revisited

The initial release of CUTE, a widely used testing environment for optimization software was described in Bongartz, Conn, Gould and Toint (1995). The latest version, now known as CUTEr is presented. New features include reorganisation of the environment to allow simultaneous multi-platform installation, new tools for, and interfaces to, optimization packages, and a considerably simplified and entirely automated installation procedure for unix systems. The SIF decoder, which used to be a part of CUTE, has become a separate tool, easily callable by various packages. It features simple extensions to the SIF test problem format and the generation of les suited to automatic differentiation packages