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Advisor(s)
Abstract(s)
In real optimization problems, usually the analytical expression of the objective function is not known, nor
its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where
the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search
Methods or Derivative-free Methods are one solution.
When the problem has constraints, penalty functions are often used. Unfortunately the choice of the
penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics
strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces
a function that aggregates the constrained violations and constructs a biobjective problem. In this problem
the step is accepted if it either reduces the objective function or the constrained violation. This implies that
the filter methods are less parameter dependent than a penalty function.
In this work, we present a new direct search method, based on simplex methods, for general constrained
optimization that combines the features of the simplex method and filter methods. This method does not
compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of
simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We
illustrate the behavior of our algorithm through some examples. The proposed methods were implemented
in Java.
Description
Keywords
Nonlinear constrained optimization Filter methods Direct search methods
Citation
Publisher
Taylor & Francis