Inverse conic programming with applications

Iyengar, Garud; Kang, Wanmo

doi:10.1016/j.orl.2004.04.007

Cited by 87 publications

(68 citation statements)

References 20 publications

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“…Thus, lower bounding inequalities on ϕ(z) can be created from any feasible solution to (30). Note that this subgradient inequality is related to the point cut (29). In particular, we have the following theorem:…”

Section: Logical Benders Decompositionmentioning

confidence: 96%

“…Inverse quadratic programs are investigated in [57,58]. Inverse conic programs are considered in [29] and inverse linear complementarity problems in [49].…”

Section: Inverse Convex Quadratic Programmingmentioning

confidence: 99%

“…If we abuse notation and allow (λ,ū,v ) to represent the ray whenz is infeasible then the ray cut is also of the form (29). These point and ray cuts should be sparsified if possible, in order to strengthen them: the fewer terms that appear in the constraint, the larger the number of binary vectors that violate it.…”

Section: Logical Benders Decompositionmentioning

confidence: 99%

“…If the optimal dual solution only has positive components of u i and v j for the bounded variables then the subgradient cut (31) can be used; otherwise the point cut (29) can be added to the master problem.…”

Section: Logical Benders Decompositionmentioning

confidence: 99%

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On linear programs with linear complementarity constraints

Mitchell

Pang

et al. 2011

J Glob Optim

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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 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.It is our great pleasure to dedicate this work to Professor Richard W. Cottle on the occasion of his 75th birthday in 2009. Professor Cottle is the father of the linear complementarity problem (LCP) [16]. The linear program with linear complementarity constraints (LPCC) treated in this paper is a natural extension of the LCP; our hope is that the LPCC will one day become as fundamental as the LCP, thereby continuing Professor Cottle's legacy, bringing it to new heights, and extending its breadth. 123 30 J Glob Optim (2012) 53:29-51We 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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Section: Logical Benders Decompositionmentioning

confidence: 96%

“…Inverse quadratic programs are investigated in [57,58]. Inverse conic programs are considered in [29] and inverse linear complementarity problems in [49].…”

Section: Inverse Convex Quadratic Programmingmentioning

confidence: 99%

Section: Logical Benders Decompositionmentioning

confidence: 99%

Section: Logical Benders Decompositionmentioning

confidence: 99%

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On linear programs with linear complementarity constraints

Mitchell

Pang

et al. 2011

J Glob Optim

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“…Burton and Toint (1992) [3] first investigated an inverse shortest paths problem, since then there are many important contributions to inverse optimization and a large number of inverse combinatorial optimization problems have been studied, see the survey paper by Heuberger [6] and the references [1,2,4], etc. For continuous optimization, Zhang and Liu [14,15] first studied inverse linear programming, Iyengar and Kang [7] discussed inverse conic programming models and their applications in portfolio optimization. And recently, Zhang and Zhang [16] studied the rate of convergence of the augmented Lagrangian method for a type of inverse quadratic programming (IQP) problems.…”

Section: Introductionmentioning

confidence: 99%

Solving a Class of Inverse QP Problems by a Smoothing Newton Method

Xiao¹,

Zhang²

2009

JCM

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We consider an inverse quadratic programming (IQP) problem in which the parameters in the objective function of a given quadratic programming (QP) problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. This problem can be formulated as a minimization problem with a positive semidefinite cone constraint and its dual (denoted IQD(A, b)) is a semismoothly differentiable (SC 1 ) convex programming problem with fewer variables than the original one. In this paper a smoothing Newton method is used for getting a Karush-Kuhn-Tucker point of IQD(A, b). The proposed method needs to solve only one linear system per iteration and achieves quadratic convergence. Numerical experiments are reported to show that the smoothing Newton method is effective for solving this class of inverse quadratic programming problems.Mathematics subject classification: 90C20, 90C25, 90C90.

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Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography

Dempe

2020

Springer Optimization and Its Applications

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Inverse conic programming with applications

Cited by 87 publications

References 20 publications

On linear programs with linear complementarity constraints

On linear programs with linear complementarity constraints

Solving a Class of Inverse QP Problems by a Smoothing Newton Method

Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography

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