Nonmonotone Feasible Direction Method For Constrained Optimization

Many nonlinear programming models arise from our practical problems,such as traffic science,telecommunications,petroleum industry,chemical industries,economics,biology,military,management science.There are various methods for nonlinear programming problems,sequence quadratic programming method,Newton's method,penalty function method,feasible direction method and so on.One of the most effective methods is feasible direction approach.The feasible direction methods have received lots of attention because their important advantages such as the descent property,feasibility of all iterations,computational efficiency and so on.Line search technique is often used in most of the feasible direction methods.But this method requires monotonically decreasing of the objective function values at each iteration which slows the rate of convergence in the presence of a narrow valley,and even result on the disconvergence.To avoid the above shortcomings,Grippo etc.proposed a nonmonotone line search in 1986.Different from the monotonic one,the value of the objective function in nonmonotone methods is permitted to increase among finite iterations.Hence the small step length or “Z” font iterations can be avoided to a certain degree when the trial points fell into the “very narrow valley”.By the modification of nonmonotone techniques and combination of the existing feasible direction,two kinds of nonmonotone feasible direction methods for constrained optimization are proposed in this paper.The main content of this paper is as follows.First,based on the existing direction methods and nonmonotone line search techniques,we propose two kinds of nonmonotone feasible direction methods.Second,by convex combination,we present a new nonmonotone line search technique which is a generalization of traditional nonmonotone search methods,and numerical experiments show that our method is better than previous nonmonotone line search techniques in some problems.In the design process of the algorithm,we avoid the penalty function and filter method.Therefore,compared with the existing methods,our method is more flexible and easier to implement.Finally,under some reasonable conditions,we prove the convergence properties of the proposed algorithms,and then,give some numerical experiments results to show our methods is better than the existing monotone feasible direction method.