In this paper, we introduce and analyze a hybrid steepest-descent extragradient algorithm for solving triple hierarchical pseudomonotone variational inequalities in a real Hilbert space. The proposed algorithm is based on Korpelevich’s extragradient method, Mann’s iteration method, hybrid steepest-descent method and Halpern’s iteration method. Under mild conditions, the strong convergence of th...

We introduce a new optimization strategy to compute numerical approximations of minimizers for optimal control problems governed by scalar conservation laws in the presence of shocks. We focus on the 1 − d inviscid Burgers equation. We first prove the existence of minimizers and, by a Γ-convergence argument, the convergence of discrete minima obtained by means of numerical approximation schemes...

In this paper we use steepest descent method for solving zero-one nonlinear programming problem. Using penalty function we transform this problem to an unconstrained optimization problem and then by steepest descent method we obtain the original problem optimal solution. 2007 Elsevier Inc. All rights reserved.