Parallel LQP alternating direction method for solving variational inequality problems with separable structure

In this paper, we propose a logarithmic-quadratic proximal alternating direction method for structured variational inequalities. The predictor is obtained by solving series of related systems of nonlinear equations, and the new iterate is obtained by a convex combination of the previous point and the one generated by a projection-type method along a new descent direction. Global convergence of the new method is proved under certain assumptions. Preliminary numerical experiments are included to verify the theoretical assertions of the proposed method.Qatar University Start-Up Grant: QUSG-CAS-DMSP-13/14-8.Scopu

Research on closed-loop supply chain network equilibrium with two-type suppliers, risk-averse manufacturers and capacity constraints

Purpose: the aim of this paper is to investigate the closed-loop supply chain (CLSC) network equilibrium wiht the consideration of three practical factors: two complementary types of suppliers, risk-averse character of the manufacturer and capacity constraints of the suppliers. Design/methodology/approach: The equilibrium of various decision makers including the suppliers, the manufacturers, the retailers, the collectors and the demand markets are modeled via finite-dimensional variational inequality, respectively. Then the governing CLSC network equilibrium model is established. The logarithmic-quadratic proximal prediction-correction algorithm is designed to solve the variational inequality model. Numerical examples are given to analyze the impact of return rate, risk-averse degree and capacity constraints on the network equilibrium under different product BOMs. Findings: with the increase of return rate, the profits of various channel members and the performance of the CLSC system will improve. There is a contradiction between profit maximization and risk minimization for the manufacturers. Moreover, the economic behavior of the CLSC is likely to be limited by the capacity constraints of the suppliers. Originality/value: Prior to this paper, few papers have addressed with the CLSC network equilibrium considering some practical factors. They assume all the suppliers are identical and all the decision-makers are risk neutral. Furthermore, the production capacities of all suppliers are assumed to be infinite or large enough. To fill the gap, this paper examines the influences of two-type suppliers, risk aversion and capacity constraints upon the CLSC network equilibrium.Peer Reviewe

An Asymmetric Proximal Decomposition Method for Convex Programming with Linearly Coupling Constraints

The problems studied are the separable variational inequalities with linearly coupling constraints. Some existing decomposition methods are very problem specific, and the computation load is quite costly. Combining the ideas of proximal point algorithm (PPA) and augmented Lagrangian method (ALM), we propose an asymmetric proximal decomposition method (AsPDM) to solve a wide variety separable problems. By adding an auxiliary quadratic term to the general Lagrangian function, our method can take advantage of the separable feature. We also present an inexact version of AsPDM to reduce the computation load of each iteration. In the computation process, the inexact version only uses the function values. Moreover, the inexact criterion and the step size can be implemented in parallel. The convergence of the proposed method is proved, and numerical experiments are employed to show the advantage of AsPDM

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more