Separated Continuous Conic Programming: Strong Duality and an Approximation Algorithm

Motivated by recent applications in robust optimization and in sign-constrained linear-quadratic control, we study in this paper a new class of optimization problems called separated continuous conic programming (SCCP). Focusing on a symmetric primal-dual pair, we develop a strong duality theory for...

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Published in:SIAM journal on control and optimization Vol. 48; no. 4; pp. 2118 - 2138
Main Authors: Wang, Xiaoqing, Zhang, Shuzhong, Yao, David D.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2009
Subjects:
Algorithms
Approximation
Conics
Discretization
Focusing
Mathematical analysis
Optimization
Optimization algorithms
Programming
Quadratic programming
Studies
ISSN:0363-0129, 1095-7138
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Abstract Motivated by recent applications in robust optimization and in sign-constrained linear-quadratic control, we study in this paper a new class of optimization problems called separated continuous conic programming (SCCP). Focusing on a symmetric primal-dual pair, we develop a strong duality theory for the SCCP. Our idea is to use discretization to connect the SCCP and its dual to two ordinary conic programs. We show if the latter are strongly feasible and with finite optimal values, a condition that is readily verifiable, then the strong duality holds for the SCCP. This approach also leads to a polynomial-time approximation algorithm that solves the SCCP to any required accuracy. [PUBLICATION ABSTRACT]
AbstractList Motivated by recent applications in robust optimization and in sign-constrained linear-quadratic control, we study in this paper a new class of optimization problems called separated continuous conic programming (SCCP). Focusing on a symmetric primal-dual pair, we develop a strong duality theory for the SCCP. Our idea is to use discretization to connect the SCCP and its dual to two ordinary conic programs. We show if the latter are strongly feasible and with finite optimal values, a condition that is readily verifiable, then the strong duality holds for the SCCP. This approach also leads to a polynomial-time approximation algorithm that solves the SCCP to any required accuracy.
Motivated by recent applications in robust optimization and in sign-constrained linear-quadratic control, we study in this paper a new class of optimization problems called separated continuous conic programming (SCCP). Focusing on a symmetric primal-dual pair, we develop a strong duality theory for the SCCP. Our idea is to use discretization to connect the SCCP and its dual to two ordinary conic programs. We show if the latter are strongly feasible and with finite optimal values, a condition that is readily verifiable, then the strong duality holds for the SCCP. This approach also leads to a polynomial-time approximation algorithm that solves the SCCP to any required accuracy. [PUBLICATION ABSTRACT]
Author Yao, David D.
Zhang, Shuzhong
Wang, Xiaoqing
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SubjectTerms Algorithms
Approximation
Conics
Discretization
Focusing
Mathematical analysis
Optimization
Optimization algorithms
Programming
Quadratic programming
Studies
Title Separated Continuous Conic Programming: Strong Duality and an Approximation Algorithm
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