A modified QP-free feasible method

AbstractIn this paper, we presented a modified QP-free filter method based on a new piecewise linear NCP functions. In contrast with the existing QP-free methods, each iteration in this algorithm only needs to solve systems of linear equations which are derived from the equality part in the KKT first order optimality conditions. Its global convergence and local superlinear convergence are obtained under mild conditions

A penalty-function-free line search SQP method for nonlinear programming

AbstractWe 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

A new filter QP-free method for the nonlinear inequality constrained optimization problem

Abstract In this paper, a filter QP-free infeasible method with nonmonotone line search is proposed for minimizing a smooth optimization problem with smooth inequality constraints. This proposed method is based on the solution of nonsmooth equations, which are obtained by the Lagrangian multiplier method and the function of the nonlinear complementarity problem for the Karush–Kuhn–Tucker optimality conditions. Especially, each iteration of this method can be viewed as a perturbation of a Newton or quasi-Newton iteration on both the primal and dual variables for the solution of the Karush–Kuhn–Tucker optimality conditions. What is more, it is considered to use the function of the nonlinear complementarity problem in the filter, which makes the proposed algorithm avoid the incompatibility. Then the global convergence of the proposed method is given. And under some mild conditions, the superlinear convergence rate can be obtained. Finally, some preliminary numerical results are shown to illustrate that the proposed filter QP-free infeasible method is quite promising

AN INFEASIBLE SSLE FILTER ALGORITHM FOR GENERAL CONSTRAINED OPTIMIZATION WITHOUT STRICT COMPLEMENTARITY

In this paper, we propose a new sequential systems of linear equations (SSLE) filter algorithm, which is an infeasible QP-free method. The new algorithm needs to solve a few reduced systems of linear equations with the same nonsingular coefficient matrix, and after finitely many iterations, only two linear systems need to be solved. Furthermore, the nearly active set technique is used to improve the computational effect. Under the linear independence condition, the global convergence is proved. In particular, the rate of convergence is proved to be one-step superlinear without assuming the strict complementarity condition. Numerical results and comparison with other algorithms indicate that the new algorithm is promising.SSLE, line search, strict complementarity, global convergence, superlinear convergence