-
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...
-
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...
-
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...
-
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...
-
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 ...
-
作者：Anitescu, M
作者单位：United States Department of Energy (DOE); Argonne National Laboratory
摘要：We present a time-stepping method to simulate rigid multibody dynamics with inelastic collision, contact, and friction. The method progresses with fixed time step without backtracking for collision and solves at every step a strictly convex quadratic program. We prove that a solution sequence of the method converges to the solution of a measure differential inclusion. We present numerical results for a few examples, and we illustrate the difference between the results from our scheme and previ...
-
作者：Bienstock, D; Zuckerberg, M
作者单位：Columbia University
摘要：Consider a 0/1 integer program min{c(T) x : Ax >= b, x epsilon {0, 1}(n)} where A is nonnegative. We show that if the number of minimal covers of Ax >= b is polynomially bounded, then for any epsilon > 0 and any fixed q, there is a polynomially large lift-and-project relaxation whose value is at least (1 - epsilon) times the value of the rank <= q relaxation. A special case of this result is that given by set-covering problems, or, generally, problems where the coefficients in A and b are boun...
-
作者：Erdogan, E; Iyengar, G
作者单位：Columbia University
摘要：In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set Q of the distributions is of the form Q = {Q : rho(p) (Q, Q(0)) <= beta}, where rho(p) denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled problem where each constraint is a robust constraint centered at a sample drawn according...
-
作者：Guan, YP; Ahmed, S; Nemhauser, GL; Miller, AJ
作者单位：University System of Georgia; Georgia Institute of Technology; University of Wisconsin System; University of Wisconsin Madison
摘要：This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical (l, S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the (l, S) inequalities to a general class of valid inequalities, called the ( Q, S-Q) inequalities, and we establish necessary and sufficient conditions which guarantee that the ( Q, S-Q) inequalities ...
-
作者：Bastin, Fabian; Cirillo, Cinzia; Toint, Philippe L.
作者单位：University of Namur
摘要：Monte Carlo methods have extensively been used and studied in the area of stochastic programming. Their convergence properties typically consider global minimizers or first-order critical points of the sample average approximation (SAA) problems and minimizers of the true problem, and show that the former converge to the latter for increasing sample size. However, the assumption of global minimization essentially restricts the scope of these results to convex problems. We review and extend the...
