-
作者：Sun, Defeng; Sun, Jie
作者单位：National University of Singapore; National University of Singapore
摘要：We study analyticity, differentiability, and semismoothness of Lowner's operator and spectral functions under the framework of Euclidean Jordan algebras. In particular, we show that many optimization-related classical results in the symmetric matrix space can be generalized within this framework. For example, the metric projection operator over any symmetric cone defined in a Euclidean Jordan algebra is shown to be strongly semismooth. The research also raises several open questions, whose ans...
-
作者：Ward, Amy R.; Kumar, Sunil
作者单位：University of Southern California; Stanford University
摘要：We consider a GI/GI/1 queue with impatient customers in heavy traffic. We use the solution of an approximating singular diffusion control problem to construct an admission control policy for the queue. The approximating control problem does not admit a so-called pathwise solution. Hence, the resulting admission control policy depends on second-moment data. We prove asymptotic optimality of the constructed policy using weak-convergence methods.
-
作者：Gromoll, H. Christian; Robert, Philippe; Zwart, Bert
作者单位：University of Virginia; University System of Georgia; Georgia Institute of Technology
摘要：We investigate a processor-sharing queue with renewal arrivals and generally distributed service times. Impatient jobs may abandon the queue or renege before completing service. The random time representing a job's patience has a general distribution and may be dependent on its initial service time requirement. A scaling procedure that gives rise to a fluid model with nontrivial yet tractable steady state behavior is presented. This fluid model captures many essential features of the underlyin...
-
作者：Dey, Santanu S.; Richard, Jean-Philippe P.
作者单位：Purdue University System; Purdue University
摘要：In this paper, we lay the foundation for the study of the two-dimensional mixed integer infinite group problem (2DMIIGP). We introduce tools to determine if a given continuous and piecewise linear function over the two-dimensional infinite group is subadditive and to determine whether it defines a facet of 2DMIIGP. We then present two different constructions that yield the first known families of facet-defining inequalities for 2DMIIGP. The first construction uses valid inequalities of the one...
-
作者：Govindan, Srihari; Wilson, Robert
作者单位：University of Iowa; Stanford University
摘要：Metastability is a refinement of the Nash equilibria of a game derived from two conditions: embedding combines behavioral axioms called invariance and small-worlds, and continuity requires games with nearby best replies to have nearby equilibria. These conditions imply that a connected set of Nash equilibria is metastable if it is arbitrarily close to an equilibrium of every sufficiently small perturbation of the best-reply correspondence of every game in which the given game is embedded as an...
-
作者：DeMiguel, Victor; Nogales, Francisco J.
作者单位：University of London; London Business School; Universidad Carlos III de Madrid
摘要：We study two different decomposition algorithms for the general (nonconvex) partially separable nonlinear program (PSP): bilevel decomposition algorithms (BDAs) and Schur interior-point methods (SIPMs). BDAs solve the problem by breaking it into a master problem and a set of independent subproblems, forming a type of bilevel program. SIPMs, on the other hand, apply an interior-point technique to solve the problem in its original (integrated) form, but then use a Schur complement approach to so...
-
作者：Levi, Retsef; Pal, Martin; Roundy, Robin O.; Shmoys, David B.
作者单位：Massachusetts Institute of Technology (MIT); Alphabet Inc.; Google Incorporated; Cornell University; Cornell University
摘要：We consider two classical stochastic inventory control models, the periodic-review stochastic inventory control problem and the stochastic lot-sizing problem. The goal is to coordinate a sequence of orders of a single commodity, aiming to supply stochastic demands over a discrete, finite horizon with minimum expected overall ordering, holding, and backlogging costs. In this paper, we address the important problem of finding computationally efficient and provably good inventory control policies...
-
作者：Guo, Xianping
作者单位：Sun Yat Sen University
摘要：This paper deals with continuous-time Markov decision processes in Polish spaces, under an expected discounted reward criterion. The transition rates of underlying continuous-time jump Markov processes are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. We first give conditions on the controlled system's primitive data. Under these conditions we prove that the transition functions of possibly nonhomogeneous continuous-time Markov processes are regular by ...
-
作者：Goldberg, Yair
作者单位：Hebrew University of Jerusalem
摘要：The minmax in repeated games with imperfect monitoring can differ from the minmax of those games with perfect monitoring when two or more players are able to gain common information known only to themselves, and utilize this information at a later stage. Gossner and Tomala showed that in a class of such games, the minmax is given by a weighted average of the payoffs of two main strategies: one in which the information is gained, and the other in which the information is utilized. However, all ...
-
作者：Xu, Huifu; Meng, Fanwen
作者单位：University of Southampton; National University of Singapore
摘要：In this paper we discuss the sample average approximation (SAA) method for a class of stochastic programs with nonsmooth equality constraints. We derive a uniform Strong Law of Large Numbers for random compact set-valued mappings and use it to investigate the convergence of Karush-Kuhn-Tucker points of SAA programs as the sample size increases. We also study the exponential convergence of global minimizers of the SAA problems to their counterparts of the true problem. The convergence analysis ...
