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作者：Bian, Wei; Chen, Xiaojun
作者单位：Harbin Institute of Technology; Hong Kong Polytechnic University
摘要：In this paper, we consider a class of constrained optimization problems where the feasible set is a general closed convex set, and the objective function has a nonsmooth, nonconvex regularizer. Such a regularizer includes widely used SCAD, MCP, logistic, fraction, hard thresholding, and non-Lipschitz L-p penalties as special cases. Using the theory of the generalized directional derivative and the tangent cone, we derive a first order necessary optimality condition for local minimizers of the ...
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作者：He, Shuangchi; Yao, Dacheng; Zhang, Hanqin
作者单位：National University of Singapore; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; National University of Singapore
摘要：We consider a continuous-review inventory system in which the setup cost of each order is a general function of the order quantity and the demand process is modeled as a Brownian motion with a positive drift. Assuming the holding and shortage cost to be a convex function of the inventory level, we obtain the optimal ordering policy that minimizes the long-run average cost by a lower bound approach. To tackle some technical issues in the lower bound approach under the quantity-dependent setup c...
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作者：Iriarte, Benjamin
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Given an underlying undirected simple graph, we consider the set of its acyclic orientations. Each of these orientations induces a partial order on the vertices of our graph and, therefore, we can count the number of linear extensions of these posets. We want to know which choice of orientation maximizes the number of linear extensions of the corresponding poset, and this problem will be solved essentially for comparability graphs and odd cycles, presenting several proofs. The corresponding en...
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作者：De Angelis, Tiziano; Federico, Salvatore; Ferrari, Giorgio
作者单位：University of Leeds; University of Siena; University of Bielefeld
摘要：This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity, as two independent one-dimensional regular diffusions, and we consider a general convex running cost function. The optimization problem is set as a three-dimensional degenerate singular stochastic control problem. We provide the optimal control as the solut...
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作者：Averkov, Gennadiy; Kruempelmann, Jan; Weltge, Stefan
作者单位：Otto von Guericke University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Lattice-free sets and their applications for cutting-plane methods in mixed-integer optimization have been studied in recent literature. The family of all integral lattice-free polyhedra that are not properly contained in another integral lattice-free polyhedron has been of particular interest. We call these polyhedra Z(d)-maximal. For fixed d, the family of Z(d)-maximal integral lattice-free polyhedra is finite up to unimodular equivalence. In view of possible applications in cutting-plane th...
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作者：Dutting, Paul; Gkatzelis, Vasilis; Roughgarden, Tim
作者单位：University of London; London School Economics & Political Science; Drexel University; Stanford University
摘要：Deferred-acceptance auctions are mechanisms whose allocation rule can be implemented using an adaptive reverse greedy algorithm. Milgrom and Segal recently introduced these auctions and proved that they satisfy remarkable incentive guarantees: in addition to being dominant strategy and incentive compatible, they are weakly group-strategyproof and can be implemented by ascending-clock auctions. Neither forward greedy mechanisms nor the VCG mechanism generally possess any of these additional inc...
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作者：Horst, Ulrich; Paulsen, Michael
作者单位：Humboldt University of Berlin
摘要：We define a stochastic model of a two-sided limit order book in terms of its key quantities best bid [ask] price and the standing buy [sell] volume density. For a simple scaling of the discreteness parameters, that keeps the expected volume rate over the considered price interval invariant, we prove a limit theorem. The limit theorem states that, given regularity conditions on the random order flow, the key quantities converge in probability to a tractable continuous limiting model. In the lim...
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作者：Kolokoltsov, Vassili
作者单位：University of Warwick
摘要：In this paper we extend the framework of the evolutionary inspection game put forward recently by the author and coworkers to a large class of conflict interactions to address the pressure executed by the major player (or principal) on the large group of small players who can resist this pressure or collaborate with the major player. We prove rigorous results on the convergence of various Markov decision models of interacting small agents (including evolutionary growth), i.e., pairwise, in gro...
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作者：Amarante, Massimiliano
作者单位：Universite de Montreal; Universite de Montreal
摘要：The concept of ambiguity designates those situations where the information available to the decision maker is insufficient to form a probabilistic view of the world. Thus, it has provided the motivation for departing from the subjective expected utility (SEU) paradigm. Yet, the formalization of the concept is missing. This is a grave omission as it leaves nonexpected utility models hanging on shaky ground. In particular, it leaves unanswered basic questions such as the following: (1) Does ambi...
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作者：Sviridenko, Maxim; Vondrak, Jan; Ward, Justin
作者单位：Yahoo! Inc; Stanford University; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a monotone increasing submodular function or minimize a monotone decreasing supermodular function with a bounded total curvature c. Intuitively, the parameter c represents how nonlinear a function f is: when c = 0, f is linear, while for c = 1, f may be an arbitrary monotone increasing...
