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SecondOrder Cone Programming
 MATHEMATICAL PROGRAMMING
, 2001
"... In this paper we survey the second order cone programming problem (SOCP). First we present several applications of the problem in various areas of engineering and robust optimization problems. We also give examples of optimization problems that can be cast as SOCPs. Next we review an algebraic struc ..."
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Cited by 237 (11 self)
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In this paper we survey the second order cone programming problem (SOCP). First we present several applications of the problem in various areas of engineering and robust optimization problems. We also give examples of optimization problems that can be cast as SOCPs. Next we review an algebraic
Applications of Secondorder Cone Programming
, 1998
"... In a secondorder cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of secondorder (quadratic) cones. SOCPs are nonlinear convex problems that include linear and (convex) quadratic programs as special cases, but are less general than semidefin ..."
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Cited by 215 (10 self)
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In a secondorder cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of secondorder (quadratic) cones. SOCPs are nonlinear convex problems that include linear and (convex) quadratic programs as special cases, but are less general than
An Algorithm for Perturbed Secondorder Cone Programs
, 2004
"... The secondorder cone programming problem is reformulated into several new systems of nonlinear equations. Assume the perturbation of the data is in a certain neighborhood of zero. Then starting from a solution to the old problem, the semismooth Newton’s iterates converge Qquadratically to a soluti ..."
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Cited by 2 (2 self)
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The secondorder cone programming problem is reformulated into several new systems of nonlinear equations. Assume the perturbation of the data is in a certain neighborhood of zero. Then starting from a solution to the old problem, the semismooth Newton’s iterates converge Qquadratically to a
Secondorder cone programming
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution
Multiple kernel learning, conic duality, and the SMO algorithm
 In Proceedings of the 21st International Conference on Machine Learning (ICML
, 2004
"... While classical kernelbased classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimiz ..."
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Cited by 443 (31 self)
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; moreover, the sequential minimal optimization (SMO) techniques that are essential in largescale implementations of the SVM cannot be applied because the cost function is nondifferentiable. We propose a novel dual formulation of the QCQP as a secondorder cone programming problem, and show how to exploit
Perturbation analysis of secondorder cone programming problems
 Mathematical Programming
, 2005
"... We discuss first and second order optimality conditions for nonlinear secondorder cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong regular ..."
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Cited by 15 (0 self)
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We discuss first and second order optimality conditions for nonlinear secondorder cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong
An active set method for singlecone secondorder cone programs
 SIAM J. on Optimization
, 2006
"... We develop an active set method for solving secondorder cone programs that may have an arbitrary number of linear constraints but are restricted to have only one secondorder cone constraint. Problems of this form arise in the context of robust optimization and trust region methods. The proposed ac ..."
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Cited by 2 (0 self)
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active set method exploits the fact that a secondorder cone program with only one secondorder cone constraint and no inequality constraints can be solved in closed form. 1
Results 1  10
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