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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Vydáno v:SIAM journal on control and optimization Ročník 48; číslo 4; s. 2118 - 2138
Hlavní autoři: Wang, Xiaoqing, Zhang, Shuzhong, Yao, David D.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2009
Témata:
Algorithms
Approximation
Conics
Discretization
Focusing
Mathematical analysis
Optimization
Optimization algorithms
Programming
Quadratic programming
Studies
ISSN:0363-0129, 1095-7138
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Shrnutí: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]
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ISSN:0363-0129
1095-7138
DOI:10.1137/060650532