A Penalty Based Filters Method in Direct Search Optimization

Constrained nonlinear optimization problems can be solved using penalty or barrier functions. This strategy, based on solving unconstrained problems obtained form the original problem, has shown to be effective, particularly when used with direct search methods. An alternative to solve the above mentioned problems is the filters method. The filters method, introduced by Fletcher and Leyffer in 2002, has been widely used to solve constrained problems. These methods use a different strategy when compared with penalty or barrier functions. The previous functions define a new one that combine the objective function and the constraints, while the filters method treat optimization problems as bi-objective problems where the objective function and a function that aggregates the constraints are optimized. Based on the work of Audet and Dennis, using filters method with derivative-free algorithms, the authors developed some works where other direct search methods were used, combining their potential with the filters method. More recently, a new variant of these methods was presented, where some alternative aggregation restrictions for the construction of filters were proposed. This paper presents a variant of the filters method, more robust than the previous ones, that has been implemented with a safeguard procedure where values of the function and constraints are linked together and are not treated as completely independently