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作者：Basu, Amitabh; Conforti, Michele; Di Summa, Marco; Paat, Joseph
作者单位：Johns Hopkins University; University of Padua; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper, we study the relationships between these two descriptions. Our results have implications for corner polyhedra. One consequence is that nonnegative, continuous valid functions suffice to describe corner polyhedra (with or without rational data).
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作者：Chen, Bohan; Blanchet, Jose; Rhee, Chang-Han; Zwart, Bert
作者单位：Stanford University; Northwestern University
摘要：We propose a class of strongly efficient ram-event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based on an importance sampling strategy that hinges on a recently established heavy-tailed sample-path large deviations result. The new estimators are straightforward to implement and can be used to systematically evaluate the probability of a wide range of rare ...
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作者：Cohen, Asaf
作者单位：University of Haifa
摘要：We consider a multidimentional Brownian control problem (BCP) with model uncertainty that formally emerges from a multiclass M/M/1 queueing control problem under heavy traffic with model uncertainty. The BCP is formulated as a multidimensional stochastic differential game with two players: a minimizer who has an equivalent role to the decision maker in the queueing control problem and a maximizer whose role is to set up the uncertainty of the model. The dynamics are driven by a Brownian motion...
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作者：Iusem, Alfredo N.; Jofre, Alejandro; Thompson, Philip
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universidad de Chile; Universidad de Chile
摘要：We consider stochastic variational inequalities (VIs) with monotone operators where the feasible set is an intersection of a large number of convex sets. We propose a stochastic approximation method with incremental constraint projections, meaning that a projection method is taken after the random operator is sampled and a component of the feasible set is randomly chosen. Such a sequential scheme is well suited for large-scale online and distributed learning. First, we assume that the VI is we...
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作者：Elie, Romuald; Mastrolia, Thibaut; Possamai, Dylan
作者单位：Universite Gustave-Eiffel; Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Saclay; Columbia University
摘要：In this paper, we investigate a moral hazard problem in finite time with lump-sum and continuous payments, involving infinitely many agents with mean-field type interactions, hired by one principal. By reinterpreting the mean-field game faced by each agent in terms of a mean-field forward-backward stochastic differential equation (FBSDE), we are able to rewrite the principal's problem as a control problem of the McKean-Vlasov stochastic differential equations. We review one general approach to...
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作者：Ahmadinejad, AmirMahdi; Dehghani, Sina; Hajiaghayi, MohammadTaghi; Loder, Brendan; Mahini, Hamid; Seddighin, Saeed
作者单位：Stanford University; University System of Maryland; University of Maryland College Park; Microsoft; University of Tehran
摘要：In the well-studied Colonel Blotto game, players must divide a pool of troops among a set of battlefields with the goal of winning a majority. Despite the importance of this game, only a few solutions for special variants of the problem are known. We provide a general technique for computing equilibria of the Colonel Blotto game. Our approach applies to variations of the Colonel Blotto game as well, including an infinite-strategy variant called the General Lotto game. We also apply our techniq...
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作者：Bruggmann, Simon; Zenklusen, Rico
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In particular, every local optimum of a constrained monotone submodular maximization problem yields a 1/2-approximation, and we also present an appropriate extension to the nonmonotone setting. Moreover, we describe a very general local search procedure that applies t...
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作者：Hungerford, James T.; Rinaldi, Francesco
作者单位：University of Padua
摘要：In this paper, we develop a general regularization-based continuous optimization framework for the maximum clique problem. In particular, we consider a broad class of regularization terms that can be included in the classic Motzkin-Straus formulation, and we develop conditions that guarantee the equivalence between the continuous regularized problem and the original one in both a global and a local sense. We further analyze, from a computational point of view, two different regularizers that s...
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作者：Burzoni, Matteo; Frittelii, Marco; Hou, Zhaoxu; Maggis, Marco; Obloj, Jan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Milan; University of Oxford
摘要：We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain abstract (pointwise) fundamental theorem of asset pricing and pricing-hedging duality. Our results are general and, in particular, cover both the so-called model independent case as well as the classical probabilistic case of Dalang-Morton-Willinger. Our ana...
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作者：Andreani, Roberto; Martinez, Jose Mario; Ramos, Alberto; Silva, Paulo J. S.
作者单位：Universidade Estadual de Campinas; Universidade Federal do Parana
摘要：Sequential optimality conditions for constrained optimization are necessarily satisfied by local minimizers, independently of the fulfillment of constraint qualifications. These conditions support the employment of different stopping criteria for practical optimization algorithms. On the other hand, when an appropriate property on the constraints holds at a point that satisfies a sequential optimality condition, such a point also satisfies the Karush-Kuhn-Tucker conditions. Those properties wi...
