Partial spectral projected gradient method with active-set strategy for linearly constrained optimization

Abstract

A method for linearly constrained optimization which modifies and generalizes recent box-constraint optimization algorithms is introduced. The new algorithm is based on a relaxed form of Spectral Projected Gradient iterations. Intercalated with these projected steps, internal iterations restricted to faces of the polytope are performed, which enhance the efficiency of the algorithms. Convergence proofs are given and numerical experiments are included and commented. Software supporting this paper is available through the Tango Project web page: http://www.ime.usp.br/∼egbirgin/tango/.

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

“…Subdomain reduction and possible discarding Let W [l,ū] be a set of linear constraints valid within the subdomain [l,ū] plus linear constraints satisfied by the global solution of (8).…”

“…For solving linear programming problems we use subroutine simplx from the Numerical Recipes in Fortran [40]. To solve the linearly constrained optimization problems, we use Genlin [8], an active-set method for linearly constrained optimization based on a relaxed form of Spectral Projected Gradient iterations intercalated with internal iterations restricted to faces of the polytope. Genlin modifies and generalizes recently introduced box-constraint optimization algorithms [13].…”

“…The number within parentheses is the number of linear constraints. "It" is the number of iterations of Algorithm 2.1 (outer iterations) which is equal to the number of subproblems (8) that are solved to ε k -global optimality using the αBB approach, and "#Nodes" is the total number of iterations of Algorithm 4.1 (inner iterations).…”

Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming

“…For solving linear programming problems we use subroutine simplx from the Numerical Recipes in Fortran [60]. To solve the linearly constrained optimization problems, we use Genlin [13], an active-set method for linearly constrained optimization based on a relaxed form of Spectral Projected Gradient iterations intercalated with internal iterations restricted to faces of the polytope. Genlin generalizes the boxconstraint optimization method Gencan [23].…”

Métodos de programação quadrática convexa esparsa e suas aplicações em projeções em poliedros

“…GENLIN, apresentado em Andretta et al (2010),é a implementação de um método de restrições ativas para problemas de pequeno e médio porte, que faz parte do Projeto TANGO (Trustable Algorithms for Nonlinear General Optimization)…”