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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 moment relaxation for two problems, the separation and covering problem with semi-algebraic sets generated by a polynomial of degree d. We show that (a) the optimal value of the relaxation finitely converges to the optimal value of the original problem, when the moment order r increases and (b) there exist probability measures such that the… (More)

We propose a proximal point algorithm to solve LAROS problem, that is the problem of finding a " large approximately rank-one submatrix ". This LAROS problem is used to sequentially extract features in data. We also develop a new stopping criterion for the proximal point algorithm, which is based on the duality conditions of ǫ-optimal solutions of the LAROS… (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.