Avoiding the Maratos effect by means of a nonmonotone line search I. general constrained problems
SIAM Journal on Numerical Analysis
Journal of Optimization Theory and Applications
Trust-region methods
On the Global Convergence of a Filter--SQP Algorithm
SIAM Journal on Optimization
Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming
SIAM Journal on Optimization
A Pattern Search Filter Method for Nonlinear Programming without Derivatives
SIAM Journal on Optimization
A globally convergent primal-dual interior-point filter method for nonlinear programming
Mathematical Programming: Series A and B
Line Search Filter Methods for Nonlinear Programming: Local Convergence
SIAM Journal on Optimization
Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence
SIAM Journal on Optimization
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We 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.