2016

最新文章

• A bundle-free implicit programming approach for a class of elliptic MPECs in function space AI翻译
  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.
• Quadratic diameter bounds for dual network flow polyhedra AI翻译
  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...
• A family of second-order methods for convex -regularized optimization AI翻译
  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...
• Lipschitz and Holder stability of optimization problems and generalized equations AI翻译
  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...
• Total variation bounds on the expectation of periodic functions with applications to recourse approximations AI翻译
  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...
• A second-order method for strongly convex -regularization problems AI翻译
  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...
• Using cuts for mixed integer knapsack sets to generate cuts for mixed integer polyhedral conic sets AI翻译
  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...
• Continuous knapsack sets with divisible capacities AI翻译
  作者：Wolsey, Laurence A.; Yaman, Hande
  作者单位：Universite Catholique Louvain; Ihsan Dogramaci Bilkent University
  摘要：We study two continuous knapsack sets and with integer, one unbounded continuous and bounded continuous variables in either or form. When the coefficients of the integer variables are integer and divisible, we show in both cases that the convex hull is the intersection of the bound constraints and polyhedra arising as the convex hulls of continuous knapsack sets with a single unbounded continuous variable. The latter convex hulls are completely described by an exponential family of partition i...
• Single-commodity robust network design with finite and Hose demand sets AI翻译
  作者：Cacchiani, Valentina; Juenger, Michael; Liers, Frauke; Lodi, Andrea; Schmidt, Daniel R.
  作者单位：University of Bologna; University of Cologne; University of Erlangen Nuremberg; Universite de Montreal; Polytechnique Montreal
  摘要：We study a single-commodity robust network design problem (sRND) defined on an undirected graph. Our goal is to determine minimum cost capacities such that any traffic demand from a given uncertainty set can be satisfied by a feasible single-commodity flow. We consider two ways of representing the uncertainty set, either as a finite list of scenarios or as a polytope. We propose a branch-and-cut algorithm to derive optimal solutions to sRND, built on a capacity-based integer linear programming...
• Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem AI翻译
  作者：Carrizo, Gabriel A.; Lotito, Pablo A.; Maciel, Maria C.
  作者单位：National University of the South; Instituto de Investigaciones en Ingenieria Electrica (IIIE); Comision Nacional de Energia Atomica (CNEA)
  摘要：A trust-region-based algorithm for the nonconvex unconstrained multiobjective optimization problem is considered. It is a generalization of the algorithm proposed by Fliege et al. (SIAM J Optim 20:602-626, 2009), for the convex problem. Similarly to the scalar case, at each iteration a subproblem is solved and the step needs to be evaluated. Therefore, the notions of decrease condition and of predicted reduction are adapted to the vectorial case. A rule to update the trust region radius is int...