-
作者：Chen, JS; Chen, X; Tseng, P
作者单位：University of Washington; University of Washington Seattle; Massachusetts Institute of Technology (MIT)
摘要：Let K-n be the Lorentz/second-order cone in R-n. For any function f from R to R, one can define a corresponding function f(soc)(x) on R-n by applying f to the spectral values of the spectral decomposition of x is an element of R-n with respect to K-n. We show that this vector-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Frechet differentiability, continuous differentiability, as well as (rho-order) semismoothness. Th...
-
作者：Henrion, R; Römisch, W
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin
摘要：We study perturbations of a stochastic program with a probabilistic constraint and r-concave original probability distribution. First we improve our earlier results substantially and provide conditions implying Holder continuity properties of the solution sets w.r.t. the Kolmogorov distance of probability distributions. Secondly, we derive an upper Lipschitz continuity property for solution sets under more restrictive conditions on the original program and on the perturbed probability measures...
-
作者：Naumann, U
作者单位：United States Department of Energy (DOE); Argonne National Laboratory
摘要：The accumulation of the Jacobian matrix F' of a vector function F : R-n --> R-m can be regarded as a transformation of its linearized computational graph into a subgraph of the directed complete bipartite graph K-n,K-m. This transformation can be performed by applying different elimination techniques that may lead to varying costs for computing F'. This paper introduces face elimination as the basic technique for accumulating Jacobian matrices by using a minimal number of arithmetic operations...
-
作者：Zhou, GL; Toh, KC
作者单位：Nanyang Technological University; Massachusetts Institute of Technology (MIT); Singapore-MIT Alliance for Research & Technology Centre (SMART); National University of Singapore
摘要：In this paper we present a primal-dual inexact infeasible interior-point algorithm for semidefinite programming problems (SDP). This algorithm allows the use of search directions that are calculated from the defining linear system with only moderate accuracy, and does not require feasibility to be maintained even if the initial iterate happened to be a feasible solution of the problem. Under a mild assumption on the inexactness, we show that the algorithm can find an epsilon-approximate soluti...
-
作者：Betrò, B
作者单位：Consiglio Nazionale delle Ricerche (CNR); Istituto di Matematica Applicata e Tecnologie Informatiche Enrico Magenes (IMATI-CNR)
摘要：An algorithm for linear semi-infinite programming is presented which accelerates the convergence of the central cutting plane algorithm first proposed in [4]. Compared with other algorithms, the algorithm in [4] has the advantage of being applicable under mild conditions and of providing feasible solutions. However its convergence has been shown to be rather slow in practical instances. The algorithm proposed in this paper introduces a simple acceleration scheme which gives faster convergence,...
-
作者：Hintermüller, M; Ulbrich, M
作者单位：University of Graz; Rice University; University of Hamburg
摘要：For a class of semismooth operator equations a mesh independence result for generalized Newton methods is established. The main result states that the continuous and the discrete Newton process, when initialized properly, converge q-linearly with the same rate. The problem class considered in the paper includes MCP-function based reformulations of first order conditions of a class of control constrained optimal control problems for partial differential equations for which a numerical validatio...
-
作者：Ulbrich, S
作者单位：Technical University of Munich
摘要：Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by Fletcher, Leyffer, and Toint [8]. Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function value in the filter together with an appropriate infeasibility measure. Moreover, it is shown that the ...
-
作者：Eskow, E; Bader, B; Byrd, R; Crivelli, S; Head-Gordon, T; Lamberti, V; Schnabel, R
作者单位：University of Colorado System; University of Colorado Boulder; United States Department of Energy (DOE); Lawrence Berkeley National Laboratory; University of California System; University of California Berkeley; University of California System; University of California Berkeley; United States Department of Energy (DOE); Lawrence Berkeley National Laboratory; United States Department of Energy (DOE); Lawrence Berkeley National Laboratory; University of California System; University of California Berkeley
摘要：We describe a large-scale, stochastic-perturbation global optimization algorithm used for determining the structure of proteins. The method incorporates secondary structure predictions (which describe the more basic elements of the protein structure) into the starting structures, and thereafter minimizes using a purely physics-based energy model. Results show this method to be particularly successful on protein targets where structural information from similar proteins is unavailable, i.e., th...
-
作者：Huang, ZH; Qi, LQ; Sun, DF
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Hong Kong Polytechnic University; National University of Singapore
摘要：Given M is an element of R-nxn and q is an element of R-n, the linear complementarity problem (LCP) is to find (x, s) is an element of R-n x R-n such that (x, s) greater than or equal to 0, s = M-x + q, x(T)s = 0. By using the Chen-Harker-Kanzow-Sniale (CHKS) smoothing function, the LCP is reformulated as a system of parameterized smooth-nonsmooth equations. As a result, a smoothing Newton algorithm, which is a modified version of the Qi-Sun-Zhou algorithm [Matheniatical Programming, Vol. 87, ...
-
作者：Murota, K; Tamura, A
作者单位：University of Tokyo; Japan Science & Technology Agency (JST); Kyoto University
摘要：A Proximity theorem is a statement that, given an optimization problem and its relaxation, an optimal solution to the original problem exists in a certain neighborhood of a solution to the relaxation. Proximity theorems have been used successfully, for example, in designing efficient algorithms for discrete resource allocation problems. After reviewing the recent results for L-convex and M-convex functions, this paper establishes Proximity theorems for larger classes of discrete convex functio...
