Parallel Variable Distribution Algorithm for Constrained Optimization with Nonmonotone Technique

Abstract

A modified parallel variable distribution (PVD) algorithm for solving large-scale constrained optimization problems is developed, which modifies quadratic subproblem $Q{P}_l$ at each iteration instead of the $Q{P}_l^{\mathrm{0}}$ of the SQP-type PVD algorithm proposed by C. A. Sagastizábal and M. V. Solodov in 2002. The algorithm can circumvent the difficulties associated with the possible inconsistency of $Q{P}_l^{\mathrm{0}}$ subproblem of the original SQP method. Moreover, we introduce a nonmonotone technique instead of the penalty function to carry out the line search procedure with more flexibly. Under appropriate conditions, the global convergence of the method is established. In the final part, parallel numerical experiments are implemented on CUDA based on GPU (Graphics Processing unit).