Three modeling paradigms in mathematical programming

• 成果类型: Article; Proceedings Paper
• 署名作者: Pang, Jong-Shi
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-010-0395-1
• 发表日期: 2010
• 页码: 297-323
• 关键词: electric-power; complementarity constraints; variational-inequalities; equilibrium constraints; relaxation algorithms; optimization problems; GLOBAL CONVERGENCE; Nash equilibria; efficiency-loss; sqp methods

摘要

Celebrating the sixtieth anniversary since the zeroth International Symposium on Mathematical Programming was held in 1949, this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field. These are: competition, dynamics, and hierarchy. The discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive, equilibrium, and nonlinear programming, and variational inequalities. We will describe the modeling approaches, mathematical formulations, and recent results of these paradigms, and sketch some open mathematical and computational challenges arising from the resulting optimization and equilibrium problems. Our goal is to elucidate the need for a systematic study of these problems and to inspire new research in the field.