Theory And Algorithm Of The Gradient Projection Method For Solving Linear Semi-infinite Programming

This paper discusses Linear Semi-Infnite Programming (LSIP) problems,which has fnite number of variables and infnitely many constraints over a com-pact metric space. Due to fairly applications in many felds, such as fnancial,games, probability and statistics, telecommunication networks and optimal pro-gramming problems, designing a feasible and efective algorithm has become a hotissue.In this paper we will focus on converting the LSIP problem into a large rangeof Linear Programming problems with fnite constraints over a compact metricspace. With this in mind and combining the Gradient Projection method andthe deepest descent method, we present an algorithm to solve the LSIP problem.Numerical experiments verify algorithms correct and efective.The essay is organized as follow.The frst chapter gives the research background and research status of theLSIP problem.The LSIP problems investigated in the second chapter in the paper has beenintroduced, and several basic theorems and defnitions of convex analysis which areessential to the optimistic problem are given. Finally some fundamental theoriesabout the Gradient Projection method are showed.The third chapter studies some characteristics of the LSIP problem, such asthe constraints systems, the structure of the feasible region, the iteration pointand the feasible region, the active constrain set, feasible descent direction and thechoice of iteration step size.Based on the above discussion, in the forth chapter, and combining betweenthe Gradient Projection method and the steepest descent method, a new GradientProjection method for solving LSIP problems has been presented. We adoptMatlab to compile the program of the presented algorithm. The results of a largeamount of experiments have showed that the presented algorithm is correct andefective.