a b s t r a c tWe propose a penalty-function-free non-monotone line search method for nonlinear optimization problems with equality and inequality constraints. This method yields global convergence without using a penalty function or a filter. Each step is required to satisfy a decrease condition for the constraint violation, as well as that for the objective function under some reasonable conditions. The proposed mechanism for accepting steps also combines the non-monotone technique on the decrease condition for the constraint violation, which leads to flexibility and an acceptance behavior comparable with filter based methods. Furthermore, it is shown that the proposed method can avoid the Maratos effect if the search directions are improved by second-order corrections (SOC). So locally superlinear convergence is achieved. We also present some numerical results which confirm the robustness and efficiency of our approach.

In this paper, we propose a new nonmonotone line search technique for unconstrained optimization problems. By using this new technique, we establish the global convergence under conditions weaker than those of the existed nonmonotone line search techniques.

In this paper, we present a nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization. Similar to Bryd-Omojokun class of algorithms, each step is composed of a quasi-normal step and a tangential step. This new method has more flexibility for the acceptance of the trial step compared to the filter methods, and requires less computational costs compared with the monotone methods. Under reasonable conditions, we give the globally convergence properties. Numerical tests are presented that confirm the efficiency of the approach.

In this paper we present a filter sequential quadratic programming (SQP) algorithm for solving constrained optimization problems. This algorithm is based on the modified quadratic programming (QP) subproblem proposed by Burke and Han, and it can avoid the infeasibility of the QP subproblem at each iteration. Compared with other filter SQP algorithms, our algorithm does not require any restoration phase procedure which may spend a large amount of computation. We underline that global convergence is derived without assuming any constraint qualifications. Preliminary numerical results are reported

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