Proximal-Like Algorithm Using the Quasi D-Function for Convex Second-Order Cone Programming

S. H. Pan () and J. S. Chen ()
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S. H. Pan: South China University of Technology
J. S. Chen: National Taiwan Normal University

Journal of Optimization Theory and Applications, 2008, vol. 138, issue 1, No 8, 95-113

Abstract: Abstract In this paper, we present a measure of distance in a second-order cone based on a class of continuously differentiable strictly convex functions on ℝ++. Since the distance function has some favorable properties similar to those of the D-function (Censor and Zenios in J. Optim. Theory Appl. 73:451–464 [1992]), we refer to it as a quasi D-function. Then, a proximal-like algorithm using the quasi D-function is proposed and applied to the second-cone programming problem, which is to minimize a closed proper convex function with general second-order cone constraints. Like the proximal point algorithm using the D-function (Censor and Zenios in J. Optim. Theory Appl. 73:451–464 [1992]; Chen and Teboulle in SIAM J. Optim. 3:538–543 [1993]), under some mild assumptions we establish the global convergence of the algorithm expressed in terms of function values; we show that the sequence generated by the proposed algorithm is bounded and that every accumulation point is a solution to the considered problem.

Keywords: Bregman functions; Quasi D-functions; Proximal-like methods; Convex second-order cone programming (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10957-008-9380-8

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