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作者：Mordukhovich, B. S.
作者单位：Wayne State University
摘要：The paper is devoted to the study of a new notion of linear suboptimality in constrained mathematical programming. This concept is different from conventional notions of solutions to optimization-related problems, while seems to be natural and significant from the viewpoint of modern variational analysis and applications. In contrast to standard notions, it admits complete characterizations via appropriate constructions of generalized differentiation in nonconvex settings. In this paper we mai...
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作者：Hager, William W.; Mair, Bernard A.; Zhang, Hongchao
作者单位：State University System of Florida; University of Florida; University of Minnesota System; University of Minnesota Twin Cities
摘要：We develop an affine-scaling algorithm for box-constrained optimization which has the property that each iterate is a scaled cyclic Barzilai-Borwein (CBB) gradient iterate that lies in the interior of the feasible set. Global convergence is established for a nonmonotone line search, while there is local R-linear convergence at a nondegenerate local minimizer where the second-order sufficient optimality conditions are satisfied. Numerical experiments show that the convergence speed is insensiti...
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作者：Mordukhovich, Boris; Nemirovski, Arkadi; Nesterov, Yurii
作者单位：University System of Georgia; Georgia Institute of Technology; Wayne State University; Universite Catholique Louvain
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作者：Barty, Kengy; Roy, Jean-Sebastien; Strugarek, Cyrille
作者单位：Electricite de France (EDF)
摘要：We focus on the numerical solution of closed-loop stochastic problems, and propose a perturbed gradient algorithm to achieve this goal. The main hurdle in such problems is the fact that the control variables are infinite-dimensional, due to, e.g., the information constraints. Alternatively said, control variables are feedbacks, i.e., functions. Such controls have hence to be represented in a finite way in order to solve the problem numerically. In the same way, the gradient of the criterion is...
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作者：Kiwiel, K. C.; Lemarechal, C.
作者单位：Inria
摘要：We give a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient values with unknown accuracy. Our approach is motivated by a number of applications in column generation, in which constraints are positively homogeneous-so that zero is a natural Slater point-and an exact oracle may be time consuming. Fina...
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作者：Babonneau, F.; Vial, J. -P.
作者单位：University of Geneva
摘要：This paper proposes an implementation of a constrained analytic center cutting plane method to solve nonlinear multicommodity flow problems. The new approach exploits the property that the objective of the Lagrangian dual problem has a smooth component with second order derivatives readily available in closed form. The cutting planes issued from the nonsmooth component and the epigraph set of the smooth component form a localization set that is endowed with a self-concordant augmented barrier....
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作者：Polyak, Roman A.
作者单位：George Mason University; George Mason University
摘要：We introduce the regularized Newton method (rnm) for unconstrained convex optimization. For any convex function, with a bounded optimal set, the rnm generates a sequence that converges to the optimal set from any starting point. Moreover the rnm requires neither strong convexity nor smoothness properties in the entire space. If the function is strongly convex and smooth enough in the neighborhood of the solution then the rnm sequence converges to the unique solution with asymptotic quadratic r...
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作者：Yin, G.; Ion, C.; Krishnamurthy, V.
作者单位：Wayne State University; University of British Columbia
摘要：Stochastic optimization/approximation algorithms are widely used to recursively estimate the optimum of a suitable function or its root under noisy observations when this optimum or root is a constant or evolves randomly according to slowly time-varying continuous sample paths. In comparison, this paper analyzes the asymptotic properties of stochastic optimization/approximation algorithms for recursively estimating the optimum or root when it evolves rapidly with nonsmooth (jump-changing) samp...
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作者：Coulonges, Sylvain; Pecher, Arnaud; Wagler, Annegret K.
作者单位：Otto von Guericke University; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS)
摘要：Perfect graphs constitute a well-studied graph class with a rich structure, which is reflected by many characterizations with respect to different concepts. Perfect graphs are, for instance, precisely those graphs G where the stable set polytope STAB(G) equals the fractional stable set polytope QSTAB(G). The dilation ratio min{t : QSTAB(G) subset of t STAB(G)} of the two polytopes yields the imperfection ratio of G. It is NP-hard to compute and, for most graph classes, it is even unknown wheth...
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作者：Auslender, Alfred; Teboulle, Marc
作者单位：Tel Aviv University; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We study subgradient projection type methods for solving non-differentiable convex minimization problems and monotone variational inequalities. The methods can be viewed as a natural extension of subgradient projection type algorithms, and are based on using non-Euclidean projection-like maps, which generate interior trajectories. The resulting algorithms are easy to implement and rely on a single projection per iteration. We prove several convergence results and establish rate of convergence ...
