Constraint Shifting Combined Homotopy Method For Solving Nonlinear Programming, Equilibrium Programming And Variational Inequalities

In this paper, we present a new method - Constraint Shifting Combined Homotopy Method (CSCH methods). Using this method, we give the CSCH equations for sovling nonlinear programming, equilibrium programming and vari-ational inequalities, and prove the existence and the global convergence of homotopy path.In Chapter 2, 3 and 4, we give the CSCH equations for solving nonlinear programming, and prove the existence and convergence of the homotopy path.Let us consider the following nonlinear programming:min f(x),s.t. g_i(x)≤0, i∈{1,...,m}.where f, g_i ∈ C~l(l > 2). Let Ω = {x|g_i(x) ≤ 0, i = 1,...,m} be its feasible region, Ω~0 = {x|g_i(x) < 0, i = 1,..., m} be its strictly feasible region.In [21], [22] and [43] Combined Homotopy Interior Point Method (abbr. CHIP method)was presented, and global convergence was proven for convex nonlinear programming without the assumption of the strict convexity of the logarithmic barrier function and for nonconvex programming under normal cone condition.