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- Dimitris Bertsimas, Xuan Vinh Doan, Karthik Natarajan, Chung-Piaw Teo
- Math. Oper. Res.
- 2010

We propose a semidefinite optimization (SDP) model for the class of minimax two-stage stochastic linear optimization problems with risk aversion. The distribution of second-stage random variables belongs to a set of multivariate distributions with known first and second moments. For the minimax stochastic problem with random objective, we provide a tight… (More)

- Dimitris Bertsimas, Xuan Vinh Doan
- European Journal of Operational Research
- 2010

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)

- Xuan Vinh Doan, Xiaobo Li, Karthik Natarajan
- Operations Research
- 2015

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)

- Xuan Vinh Doan, Stephen A. Vavasis
- SIAM Journal on Optimization
- 2013

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)

- Xuan Vinh Doan, Karthik Natarajan
- Operations Research
- 2012

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)

- Xuan Vinh Doan, Kim-Chuan Toh, Stephen A. Vavasis
- SIAM J. Scientific Computing
- 2013

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)

- Xuan Vinh Doan, Stephen A. Vavasis
- SIAM Journal on Optimization
- 2016

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)

- Xuan Vinh Doan, Serge Kruk, Henry Wolkowicz
- Optimization Methods and Software
- 2012

Current successful methods for solving semidefinite programs, SDP, are based on primal-dual interior-point approaches. These usually involve a symmetrization step to allow for application of Newton’s method followed by block elimination to reduce the size of the Newton equation. Both these steps create ill-conditioning in the Newton equation and singularity… (More)

- Dimitris Bertsimas, Xuan Vinh Doan, Jean B. Lasserre
- Oper. Res. Lett.
- 2008

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)