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作者：Aronna, M. Soledad; Bonnans, J. Frederic; Kroner, Axel
作者单位：Getulio Vargas Foundation; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Universite Paris Saclay
摘要：In this paper we consider second order optimality conditions for a bilinear optimal control problem governed by a strongly continuous semigroup operator, the control entering linearly in the cost function. We derive first and second order optimality conditions, taking advantage of the Goh transform. We then apply the results to the heat and wave equations.
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作者：Carcamo, Gabriel; Flores-Bazan, Fabian
作者单位：Universidad de Concepcion; Universidad de Concepcion
摘要：Some topological and geometric characterizations of strong duality for a non convex optimization problem under a single equality and geometric constraints are established. In particular, a hidden convexity of the conic hull of joint-range of the pair of functions associated to the original problem, is obtained. Applications to derive (a characterization of the validity of) KKT conditions without standard constraints qualification, are also discussed. It goes beyond the exact penalization techn...
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作者：Klatte, Diethard; Kummer, Bernd
作者单位：University of Zurich; Humboldt University of Berlin
摘要：We present approaches to (generalized) Newton methods in the framework of generalized equations , where f is a function and M is a multifunction. The Newton steps are defined by approximations of f and the solutions of . We give a unified view of the local convergence analysis of such methods by connecting a certain type of approximation with the desired kind of convergence and different regularity conditions for . Our paper is, on the one hand, thought as a survey of crucial parts of the topi...
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作者：Prakash, Anupam; Sikora, Jamie; Varvitsiotis, Antonios; Wei, Zhaohui
作者单位：Nanyang Technological University; National University of Singapore; Nanyang Technological University
摘要：An n x n matrix X is called completely positive semidefinite (cpsd) if there exist d x d Hermitian positive semidefinite matrices {P-i}(i=1)(n) (for some d >= 1) such that X-ij = Tr(P-i P-j), for all i, j is an element of{1,..., n}. The cpsd-rank of a cpsd matrix is the smallest d >= 1 for which such a representation is possible. In this work we initiate the study of the cpsd-rank which we motivate in two ways. First, the cpsd-rank is a natural non-commutative analogue of the completely positi...
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作者：Burke, James V.; Eaton, Julia
作者单位：University of Washington; University of Washington Seattle; University of Washington; University of Washington Tacoma
摘要：The spectral abscissa is the largest real part of an eigenvalue of a matrix and the spectral radius is the largest modulus. Both are examples of spectral max functions-the maximum of a real-valued function over the spectrum of a matrix. These mappings arise in the control and stabilization of dynamical systems. In 2001, Burke and Overton characterized the regular subdifferential of the spectral abscissa and showed that the spectral abscissa is subdifferentially regular in the sense of Clarke w...
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作者：Louveaux, Quentin; Skutella, Martin
作者单位：University of Liege; Technical University of Berlin
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作者：Singh, Mohit; Zenklusen, Rico
作者单位：Microsoft; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The notion of degree-constrained spanning hierarchies, also called k-trails, was recently introduced in the context of network routing problems. They describe graphs that are homomorphic images of connected graphs of degree at most k. First results highlight several interesting advantages of k-trails compared to previous routing approaches. However, so far, only little is known regarding computational aspects of k-trails. In this work we aim to fill this gap by presenting how k-trails can be a...
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作者：Todd, Michael J.
作者单位：Cornell University
摘要：The max-k-sum of a set of real scalars is the maximum sum of a subset of size k, or alternatively the sum of the k largest elements. We study two extensions: first, we show how to obtain smooth approximations to functions that are pointwise max-k-sums of smooth functions. Second, we discuss how the max-k-sum can be defined on vectors in a finite-dimensional real vector space ordered by a closed convex cone.
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作者：Borwein, Jonathan M.; Giladi, Ohad
作者单位：University of Newcastle
摘要：We define convexity canonically in the setting of monoids. We show that many classical results from convex analysis hold for functions defined on such groups and semigroups, rather than only vector spaces. Some examples and counter-examples are also discussed.
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作者：Kruger, Alexander Y.; Luke, D. Russell; Thao, Nguyen H.
作者单位：Federation University Australia; University of Gottingen; Can Tho University
摘要：We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between seemingly different ideas and point to possible necessary conditions for local linear convergence of fundamental algorithms.
