A Penalty-Free Method With Nonmonotone Line Search For Nonlinear Optimization

The traditional methods for solving nonlinear constrained optimization problems are penalty-type and penalty-free-type.They may suffer from the Maratos effect,which affects convergence rate of the algorithm.Nowadays,Lagrangian function method,sec-ond order correction(SOC)and nonmonotone strategy can avoid the Maratos effect SOC is a common method but cumbersome.Among nonmonotone penalty-free meth-ods,some nonmonotone filter methods still overcome the Maratos effect by SOC steps and need feasibility restoration phaseIn this paper,we propose a,new method without a penalty function or a filter for general nonlinear optimization,with nonmonotone line search technique.The search direction is some convex combination of the feasible direction and optimal direction,which can solve inconsistence of subproblems.If the objective function or the constraint violation improves sufficiently,the iteration is successful.The algorithm consists of f-type,c-type and v-type successful iterations and unsuccessful iterations.We need check the current iteration is neither f-type or c-type iteration,then estimate whether it is a v-type iteration.The new method without a penalty or a filter;without SOC steps or feasibility restoration phase;nonmonotone technique relaxes the steps acceptance conditions.Under the usual assumptions,we establish its global and local convergence Finally,numerical example shows that it can avoid the Maratos effect.