Filters method in direct search optimization, new measures to admissibility

Constrained nonlinear optimization problems are usually solved using penalty or barrier methods combined with unconstrained optimization methods. Another alternative used to solve constrained nonlinear optimization problems is the lters method. Filters method, introduced by Fletcher and Ley er in 2002, have been widely used in several areas of constrained nonlinear optimization. These methods treat optimization problem as bi-objective attempts to minimize the objective function and a continuous function that aggregates the constraint violation functions. Audet and Dennis have presented the rst lters method for derivative-free nonlinear programming, based on pattern search methods. Motivated by this work we have de- veloped a new direct search method, based on simplex methods, for general constrained optimization, that combines the features of the simplex method and lters method. This work presents a new variant of these methods which combines the lters method with other direct search methods and are proposed some alternatives to aggregate the constraint violation functions.

An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.