Abstract
In this paper, we present a flexible nonmonotone filter method for solving nonlinear constrained optimization problems which are common models in industry. This new method has more flexibility for the acceptance of the trial step compared to the traditional filter methods, and requires less computational costs compared with the monotone-type methods. Moreover, we use a self-adaptive parameter to adjust the acceptance criteria, so that Maratos effect can be avoided a certain degree. Under reasonable assumptions, the proposed algorithm is globally convergent. Numerical tests are presented that confirm the efficiency of the approach.
Highlights
IntroductionWe consider the following inequality constrained nonlinear optimization problem (P) min f (x) s.t. ci(x) ≤ , i ∈ I = { , ,
We consider the following inequality constrained nonlinear optimization problem (P) min f (x) s.t. ci(x) ≤, i ∈ I = {, . . . , m}, where x ∈ Rn, the functions f : Rn → R and ci (i ∈ I) : Rn → R are all twice continuously differentiable
Motivated by the idea and methods above, we proposed a class of nonmonotone filter trust region methods with self-adaptive parameter for solving problem (P)
Summary
We consider the following inequality constrained nonlinear optimization problem (P) min f (x) s.t. ci(x) ≤ , i ∈ I = { , , . There are various methods for solving the inequality constrained nonlinear optimization problem (P). Sequential quadratic programming methods, trust region approaches [ ], penalty methods and interior point methods [ ]. In these works, a penalty or Lagrange function is always used to test the acceptability of the iterates. In , Fletcher and Leyffer [ ] proposed a class of filter methods, which does not require any penalty parameter and has promising numerical results. Fletcher et al [ ] proved the global convergence of the filter-SQP method, Ulbrich and Ulbrich [ ] showed its superlin-
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