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作者：Bourdin, Loic; Dhar, Gaurav
作者单位：Universite de Limoges; Centre National de la Recherche Scientifique (CNRS)
摘要：In the present paper we derive a Pontryagin maximum principle for general nonlinear optimal sampled-data control problems in the presence of running inequality state constraints. We obtain, in particular, a nonpositive averaged Hamiltonian gradient condition associated with an adjoint vector being a function of bounded variation. As a well known challenge, theoretical and numerical difficulties may arise due to the possible pathological behavior of the adjoint vector (jumps and singular part l...
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作者：Xie, Weijun; Ahmed, Shabbir; Jiang, Ruiwei
作者单位：Virginia Polytechnic Institute & State University; University System of Georgia; Georgia Institute of Technology; University of Michigan System; University of Michigan
摘要：A distributionally robust joint chance constraint involves a set of uncertain linear inequalities which can be violated up to a given probability threshold epsilon, over a given family of probability distributions of the uncertain parameters. A conservative approximation of a joint chance constraint, often referred to as a Bonferroni approximation, uses the union bound to approximate the joint chance constraint by a system of single chance constraints, one for each original uncertain constrain...
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作者：Dey, Santanu S.; Luedtke, James R.; Sahinidis, Nikolaos, V
作者单位：University System of Georgia; Georgia Institute of Technology; University of Wisconsin System; University of Wisconsin Madison; University System of Georgia; Georgia Institute of Technology
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作者：Luo, Hao; Chen, Long
作者单位：Sichuan University; University of California System; University of California Irvine
摘要：Convergence analysis of accelerated first-order methods for convex optimization problems are developed from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient (NAG) flow, is derived from the connection between acceleration mechanism and A-stability of ODE solvers, and the exponential decay of a tailored Lyapunov function along with the solution trajectory is proved. Numerical discretizations of NAG flow are then considered ...
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作者：Lu, Haihao
作者单位：University of Chicago
摘要：There has been a long history of using ordinary differential equations (ODEs) to understand the dynamics of discrete-time algorithms (DTAs). Surprisingly, there are still two fundamental and unanswered questions: (i) it is unclear how to obtain a suitable ODE from a given DTA, and (ii) it is unclear the connection between the convergence of a DTA and its corresponding ODEs. In this paper, we propose a new machinery-an O(s(r))-resolution ODE framework-for analyzing the behavior of a generic DTA...
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作者：Yang, Haoxiang; Morton, David P.
作者单位：Northwestern University; The Chinese University of Hong Kong, Shenzhen
摘要：In this paper, we consider an optimization problem involving crashing an activity network under a single disruption. A disruption is an event whose magnitude and timing are random. When a disruption occurs, the duration of an activity that has yet to start-or alternatively, yet to complete-can change. We formulate a two-stage stochastic mixed-integer program, in which the timing of the stage is random. In our model, the recourse problem is a mixed-integer program. We prove the problem is NP-ha...
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作者：Kis, Tamas; Horvath, Marko
摘要：In this paper we reconsider a known technique for constructing strong MIP formulations for disjunctive constraints of the form x is an element of boolean OR(m)(i=1) P-i, where the (P)i are polytopes. The formulation is based on the Cayley Embedding of the union of polytopes, namely, Q := conv(boolean OR(m)(i=1) P-i x {epsilon(i)}), where epsilon(i) is the ith unit vector in R-m. Our main contribution is a full characterization of the facets of Q, provided it has a certain network representatio...
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作者：Pichler, Alois; Xu, Huifu
作者单位：Technische Universitat Chemnitz; University of Southampton
摘要：This paper considers distributionally robust formulations of a two stage stochastic programming problem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage. We carry out a stability analysis by looking into variations of the ambiguity set under the Wasserstein metric, decision spaces at both stages and the support set of the random variables. In the case when the risk measure is risk neutral, the stability result is presented with the variation o...
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作者：Zhao, Chen; Xiu, Naihua; Qi, Houduo; Luo, Ziyan
作者单位：Beijing Jiaotong University; University of Southampton
摘要：The sparse nonlinear programming (SNP) problem has wide applications in signal and image processing, machine learning and finance, etc. However, the computational challenge posed by SNP has not yet been well resolved due to the nonconvex and discontinuous to-norm involved. In this paper, we resolve this numerical challenge by developing a fast Newton-type algorithm. As a theoretical cornerstone, we establish a first-order optimality condition for SNP based on the concept of strong beta-Lagrang...
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作者：Nohra, Carlos J.; Raghunathan, Arvind U.; Sahinidis, Nikolaos, V
作者单位：University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct these quadratic cuts, we solve a separation problem involving a linear matrix inequality with a special structure that allows the use of specialized solution algorithms. Our quadratic cuts are nonconvex, but define a convex feasible set when intersected with th...
