Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 53, Issue 1, Pages 29-51Publisher
SPRINGER
DOI: 10.1007/s10898-010-9644-3
Keywords
Linear programs with linear complementarity constraints; Inverse programming; Hierarchical programming; Piecewise linear programming; Quantile minimization; Cross-validated support vector regression
Funding
- National Science Foundation [DMS-0715446, CMMI-0969600]
- Air Force Office of Sponsored Research [FA9550-08-1-0081, FA9550-08-1-0061]
- Office of Naval Research [N00014-06-1-0014]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [969600] Funding Source: National Science Foundation
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The paper is a manifestation of the fundamental importance of the linear program with linear complementarity constraints (LPCC) in disjunctive and hierarchical programming as well as in some novel paradigms of mathematical programming. In addition to providing a unified framework for bilevel and inverse linear optimization, nonconvex piecewise linear programming, indefinite quadratic programs, quantile minimization, and a (0) minimization, the LPCC provides a gateway to a mathematical program with equilibrium constraints, which itself is an important class of constrained optimization problems that has broad applications. We describe several approaches for the global resolution of the LPCC, including a logical Benders approach that can be applied to problems that may be infeasible or unbounded.
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