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作者：Meng, FW; Sun, DF; Zhao, GY
作者单位：University of Southampton; National University of Singapore
摘要：We show that a locally Lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point. We present a sufficient condition for the semismoothness of solutions to generalized equations over cone reducible (nonpolyhedral) convex sets. We prove that the semismoothness of solutions to the Moreau-Yosida regularization of a lower semicontinuous proper convex function is implied by the semismoothness of the metric projector over the ...
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作者：Burachik, RS; Jeyakumar, V
作者单位：Universidade Federal do Rio de Janeiro; University of New South Wales Sydney
摘要：In 1951, Fenchel discovered a special duality, which relates the minimization of a sum of two convex functions with the maximization of the sum of concave functions, using conjugates. Fenchel's duality is central to the study of constrained optimization. It requires an existence of an interior point of a convex set which often has empty interior in optimization applications. The well known relaxations of this requirement in the literature are again weaker forms of the interior point condition....
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作者：Frangioni, A; Lodi, A; Rinaldi, G
作者单位：University of Pisa; University of Bologna; Consiglio Nazionale delle Ricerche (CNR); Istituto di Analisi dei Sistemi ed Informatica Antonio Ruberti (IASI-CNR)
摘要：The semimetric polytope is an important polyhedral structure lying at the heart of several hard combinatorial problems. Therefore, linear optimization over the semimetric polytope is crucial for a number of relevant applications. Building on some recent polyhedral and algorithmic results about a related polyhedron, the rooted semimetric polytope, we develop and test several approaches, based over Lagrangian relaxation and application of Non Differentiable Optimization algorithms, for linear op...
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作者：Burke, JV; Deng, S
作者单位：University of Washington; University of Washington Seattle; Northern Illinois University
摘要：The notion of weak sharp minima is an important tool in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms designed to solve these problems. It has been studied extensively by several authors. This paper is the second of a series on this subject where the basic results on weak sharp minima in Part I are applied to a number of important problems in convex programming. In Part II we study applications to the ...
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作者：Chen, JS; Tseng, P
作者单位：National Taiwan Normal University; University of Washington; University of Washington Seattle
摘要：A popular approach to solving the nonlinear complementarity problem (NCP) is to reformulate it as the global minimization of a certain merit function over R-n. A popular choice of the merit function is the squared norm of the Fischer-Burmeister function, shown to be smooth over R-n and, for monotone NCP, each stationary point is a solution of the NCP. This merit function and its analysis were subsequently extended to the semidefinite complementarity problem (SDCP), although only differentiabil...
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作者：Burke, JV; Lewis, AS; Overton, ML
作者单位：University of Washington; University of Washington Seattle; Cornell University; New York University
摘要：The Gauss-Lucas Theorem on the roots of polynomials nicely simplifies the computation of the subderivative and regular subdifferential of the abscissa mapping on polynomials (the maximum of the real parts of the roots). This paper extends this approach to more general functions of the roots. By combining the Gauss-Lucas methodology with an analysis of the splitting behavior of the roots, we obtain characterizations of the subderivative and regular subdifferential for these functions as well. I...
