Accelerating the Levenberg-Marquardt method for the minimization of the square of functions with box constraints / Acelerando o metodo de Levenberg-Marquardt para a minimização da soma de quadrados de funções com restrições de caixa

AUTOR(ES)

Luiz Antonio da Silva Medeiros

DATA DE PUBLICAÇÃO

2008

RESUMO

In this work, we present an active set algorithm for minimizing the sum of squares of smooth functions, with box constraints. The algorithm is highly inspired in the work of Birgin and Mart´inez [4]. The differences are concentrated on the chosen search direction and on the use of an acceleration technique to update the step. At each iteration, we define an active face and solve an unconstrained quadratic subproblem using the Levenberg-Marquardt method (see [26], [28] and [33]), obtaining a descent direction and an approximate solution x+. Using only the free variables, we try to accelerate the method defining a new solution xa as a linear combination of the last p-1 approximate solutions together with x+. The coefficients of this linear combination are conveniently computed solving a constrained least squares problem that takes into account the objective function values of these p approximate solutions. Like in [4], we compute a line search and use projection techniques to add new constraints to the active set. The spectral projected gradient [5] is used to leave the current active face. Numerical experiments confirm that the algorithm is both efficient and robust

ASSUNTO(S)

levenberg-marquardt otimização matematica levenberg-marquardt metodo de mathematical optimization project gradient methods least squares metodo do gradiente projetado methods minimos quadrados

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