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作者：Cibulka, R.; Dontchev, A. L.
作者单位：University of West Bohemia Pilsen; University of West Bohemia Pilsen; University of Michigan System; University of Michigan; University of Michigan System; University of Michigan
摘要：In a recent paper, Izmailov (Math Program Ser A 147:581-590, 2014) derived an extension of Robinson's implicit function theorem for nonsmooth generalized equations in finite dimensions, which reduces to Clarke's inverse function theorem when the generalized equation is just an equation. Pales (J Math Anal Appl 209:202-220, 1997) gave earlier a generalization of Clarke's inverse function theorem to Banach spaces by employing Ioffe's strict pre-derivative. In this paper we generalize both theore...
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作者：Bai, Lijie; Mitchell, John E.; Pang, Jong-Shi
作者单位：MathWorks; Rensselaer Polytechnic Institute; University of Southern California
摘要：This paper studies several classes of nonconvex optimization problems defined over convex cones, establishing connections between them and demonstrating that they can be equivalently formulated as convex completely positive programs. The problems being studied include: a conic quadratically constrained quadratic program (QCQP), a conic quadratic program with complementarity constraints (QPCC), and rank constrained semidefinite programs. Our results do not make any boundedness assumptions on th...
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作者：Liu, Ya-Feng; Ma, Shiqian; Dai, Yu-Hong; Zhang, Shuzhong
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese University of Hong Kong; University of Minnesota System; University of Minnesota Twin Cities
摘要：The composite minimization problem over a general polyhedron has received various applications in machine learning, wireless communications, image restoration, signal reconstruction, etc. This paper aims to provide a theoretical study on this problem. First, we derive the Karush-Kuhn-Tucker (KKT) optimality conditions for local minimizers of the problem. Second, we propose a smoothing sequential quadratic programming framework for solving this problem. The framework requires a (approximate) so...
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作者：Hintermueller, M.; Surowiec, T.
作者单位：Humboldt University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Using a standard first-order optimality condition for nonsmooth optimization problems, a general framework for a descent method is developed. This setting is applied to a class of mathematical programs with equilibrium constraints in function space from which a new algorithm is derived. Global convergence of the algorithm is demonstrated in function space and the results are then illustrated by numerical experiments.
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作者：Borgwardt, Steffen; Finhold, Elisabeth; Hemmecke, Raymond
作者单位：Technical University of Munich
摘要：Both the combinatorial and the circuit diameter of polyhedra are of interest to the theory of linear programming for their intimate connection to a best-case performance of linear programming algorithms. We study the diameters of dual network flow polyhedra associated to b-flows on directed graphs and prove quadratic upper bounds for both of them: the minimum of and for the combinatorial diameter, and for the circuit diameter. Previously, bounds on these diameters have only been known for bipa...
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作者：Byrd, Richard H.; Chin, Gillian M.; Nocedal, Jorge; Oztoprak, Figen
作者单位：University of Colorado System; University of Colorado Boulder; Northwestern University; Istanbul Bilgi University
摘要：This paper is concerned with the minimization of an objective that is the sum of a convex function f and an regularization term. Our interest is in active-set methods that incorporate second-order information about the function f to accelerate convergence. We describe a semismooth Newton framework that can be used to generate a variety of second-order methods, including block active set methods, orthant-based methods and a second-order iterative soft-thresholding method. The paper proposes a n...
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作者：Gfrerer, Helmut; Klatte, Diethard
作者单位：Johannes Kepler University Linz; University of Zurich
摘要：This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lipschitz and upper Holder type, respectively, hold. Furthermore, we apply the above results to parametric mathematical programs with equilibrium constraints and demonstrate, how s...
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作者：Romeijnders, Ward; van der Vlerk, Maarten H.; Haneveld, Willem K. Klein
作者单位：University of Groningen
摘要：We derive a lower and upper bound for the expectation of periodic functions, depending on the total variation of the probability density function of the underlying random variable. Using worst-case analysis we derive tighter bounds for functions that are periodically monotone. These bounds can be used to evaluate the performance of approximations for both continuous and integer recourse models. In this paper, we introduce a new convex approximation for totally unimodular recourse models, and w...
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作者：Fountoulakis, Kimon; Gondzio, Jacek
作者单位：University of Edinburgh; University of Edinburgh; Heriot Watt University
摘要：In this paper a robust second-order method is developed for the solution of strongly convex -regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently solved. The proposed approach is a primal-dual Newton conjugate gradients (pdNCG) method. Convergence properties of pdNCG are studied and worst-case iteration complexity is established. Numerical results are presented on synthetic sparse least-squares problems a...
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作者：Sanjeevi, Sujeevraja; Masihabadi, Sina; Kianfar, Kiavash
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Based on a bijective mapping between two mixed integer sets, we introduce a new perspective on developing cuts for the mixed integer polyhedral conic (MIPC) set by establishing a one-to-one correspondence between the cuts for this set and those for a related mixed integer knapsack (MIK) set. The face/facet-defining properties of the corresponding cuts are identical for their respective sets. We further show that the cut generation approach for the MIPC set resulting from this new perspective a...
