Three modeling paradigms in mathematical programming

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...

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Bibliographic Details
Published in:Mathematical programming Vol. 125; no. 2; pp. 297 - 323
Main Author: Pang, Jong-Shi
Format: Journal Article Conference Proceeding
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.10.2010
Springer
Springer Nature B.V
Subjects:
Algorithms
Anniversaries
Applied sciences
Calculus of variations and optimal control
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Competition
Control theory
Dynamical systems
Equilibrium
Exact sciences and technology
Full Length Paper
Game theory
Hierarchies
Inequalities
Joints
Linear programming
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear programming
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Optimization
Ordinary differential equations
Paradigms
Sciences and techniques of general use
Studies
Theoretical
90-02
90C33
Momentum
Complementarity problem
Non linear programming
Equilibrium condition
Modeling
Optimization
Hierarchized structure
Hierarchy
Variational inequality
Disjunctive programming
Mathematical programming
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-010-0395-1