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作者：Aghassi, M; Bertsimas, D
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We present a distribution-free model of incomplete-information games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our robust game'' model relaxes the assumptions of Harsanyi's Bayesian game model, and provides an alternative distribution-free equilibrium concept, which we call robust-optimization equilibrium,'' to that of the ex post equilibrium. We prove that the robust-optimization equilibria of an inc...
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作者：Michaels, D; Weismantel, R
作者单位：Otto von Guericke University
摘要：This paper deals with the reformulation of a polynomial integer program. For deducing a linear integer relaxation of such a program a class of polyhedra that are associated with nonlinear functions is introduced. A characterization of the family of polynomials for which our approach leads to an equivalent linear integer program is given. Finally the family of so-called integer-convex polynomials is defined, and polyhedra related to such a polynomial are investigated.
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作者：Dash, S; Günlük, O
作者单位：International Business Machines (IBM); IBM USA
摘要：In this paper we use facets of simple mixed-integer sets with three variables to derive a parametric family of valid inequalities for general mixed-integer sets. We call these inequalities two-step MIR inequalities as they can be derived by applying the simple mixed-integer rounding (MIR) principle of Wolsey (1998) twice. The two-step MIR inequalities define facets of the master cyclic group polyhedron of Gomory (1969). In addition, they dominate the strong fractional cuts of Letchford and Lod...
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作者：Silva, Eduardo F.; Wood, R. Kevin
作者单位：United States Department of Defense; United States Navy; Naval Postgraduate School
摘要：We begin this paper by identifying a class of stochastic mixed-integer programs that have column-oriented formulations suitable for solution by a branch-and-price algorithm (B&P). We then survey a number of examples, and use a stochastic facility-location problem (SFLP) for a detailed demonstration of the relevant modeling and solution techniques. Computational results with a scenario representation of uncertain costs, demands and capacities show that B&P can be orders of magnitude faster than...
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作者：Malik, U; Jaimoukha, IM; Halikias, GD; Gungah, SK
作者单位：Imperial College London; City St Georges, University of London
摘要：Consider the semidefinite relaxation (SDR) of the quadratic integer program (QIP): gamma := max {x(T) Qx : x is an element of {-1, 1}(n)} <= min {trace(D) : D - Q greater than or similar to 0} =: (gamma) over bar where Q is a given symmetric matrix and D is diagonal. We consider the SDR gap (gamma) over bar gamma. We establish the uniqueness of the SDR solution and prove that gamma = (gamma) over bar if and only if gamma(r) := n(-1) max {x(T) VVT x : x is an element of {-1, 1}(n)} = 1 where V ...
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作者：Beck, A; Ben-Tal, A; Eldar, YC
作者单位：Technion Israel Institute of Technology; Technion Israel Institute of Technology
摘要：This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in which the second order statistics of the noise vectors (i.e., their covariance matrices) are also subjected to un...
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作者：Roman, Diana; Darby-Dowman, Ken; Mitra, Gautam
作者单位：Brunel University
摘要：Mean-risk models have been widely used in portfolio optimization. However, such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio which is non-dominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties. The problem is multi-objective and is transformed int...
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作者：Dentcheva, Darinka; Ruszczynski, Andrzej
作者单位：Stevens Institute of Technology; Rutgers University System; Rutgers University New Brunswick
摘要：We consider optimization problems with second order stochastic dominance constraints formulated as a relation of Lorenz curves. We characterize the relation in terms of rank dependent utility functions, which generalize Yaari's utility functions. We develop optimality conditions and duality theory for problems with Lorenz dominance constraints. We prove that Lagrange multipliers associated with these constraints can be identified with rank dependent utility functions. The problem is numericall...
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作者：Bertsimas, Dimitris; Caramanis, Constantine
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：Using recent progress on moment problems, and their connections with semidefinite optimization, we present in this paper a new methodology based on semidefinite optimization, to obtain a hierarchy of upper and lower bounds on linear functionals defined on solutions of linear partial differential equations. We apply the proposed method to examples of PDEs in one and two dimensions, with very encouraging results. We pay particular attention to a PDE with oblique derivative conditions, commonly a...
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作者：Kaul, H; Jacobson, SH
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：The Kauffman NK model has been used in theoretical biology, physics and business organizations to model complex systems with interacting components. Recent NK model results have focused on local optima. This paper analyzes global optima of the NK model. The resulting global optimization problem is transformed into a stochastic network model that is closely related to two well-studied problems in operations research. This leads to applicable strategies for explicit computation of bounds on the ...
