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In this paper, we propose a semidefinite optimization (SDP) based model for the class of minimax two-stage stochastic linear optimization problems with risk aversion. The distribution of the second-stage random variables is assumed to be chosen from a set of multivariate distributions with known mean and second moment matrix. For the minimax stochastic… (More)

We propose a convex optimization formulation with the nuclear norm and 1-norm to find a large approximately rank-one submatrix of a given nonnegative matrix. We develop optimality conditions for the formulation and characterize the properties of the optimal solutions. We establish conditions under which the optimal solution of the convex formulation has a… (More)

Given a combinatorial optimization problem with an arbitrary partition of the set of random objective coefficients, we evaluate the tightest possible bound on the expected optimal value for joint distributions consistent with the given multivariate marginals of the subsets in the partition. For univariate marginals, this bound was first proposed by… (More)

In this paper, we develop a distributionally robust portfolio optimization model where the robustness is to different dependency structures among the random losses. For a Fréchet class of distributions with overlapping marginals, we show that the distributionally robust portfolio optimization problem is efficiently solvable with linear programming. To… (More)

We propose both robust and data-driven approaches to a fluid model of call centers that incorporates random arrival rates with abandonment to determine staff levels and dynamic routing policies. Resulting models are tested with real data obtained from the call center of a US bank. Computational results show that the robust fluid model is significantly more… (More)

We propose a convex optimization formulation with the Ky Fan 2-k-norm and 1-norm to find k largest approximately rank-one submatrix blocks of a given nonnegative matrix that has low-rank block diagonal structure with noise. We analyze low-rank and sparsity structures of the optimal solutions using properties of these two matrix norms. We show that, under… (More)

We propose a method to calculate lower and upper bounds of some exponential multivariate integrals using moment relaxations and show that they asymptotically converge to the value of the integrals when the moment degree increases. We report computational results for integrals involving the normal distribution and exponential order statistic probabilities.

We study the problem of moments and present two diverse applications that apply both the hierarchy of moment relaxation and the moment duality theory. We then propose a moment-based uncertainty model for stochastic optimization problems, which addresses the ambiguity of probability distributions of random parameters with a minimax decision rule. We… (More)

We propose a method to approximate a class of exponential multivariate integrals using moment relaxations. Using this approach, both lower and upper bounds of the integrals are obtained and we show that these bound values asymptotically converge to the real value of the integrals when the moment degree r increases. We further demonstrate the method by… (More)