Price of Anarchy for Non-atomic Congestion Games with Stochastic Demands

We generalize the notions of user equilibrium and system optimum to non-atomic congestion games with stochastic demands. We establish upper bounds on the price of anarchy for three different settings of link cost functions and demand distributions, namely, (a) affine cost functions and general distributions, (b) polynomial cost functions and general positive-valued distributions, and (c) polynomial cost functions and the normal distributions. All the upper bounds are tight in some special cases, including the case of deterministic demands.Comment: 31 page

Finding the largest low-rank clusters with Ky Fan 2-k-norm and l1-norm

We propose a convex optimization formulation with the Ky Fan 2-k-norm and l1-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 certain hypotheses, with high probability, the approach can recover rank-one submatrix blocks even when they are corrupted with random noise and inserted into a much larger matrix with other random noise blocks

Low-rank matrix recovery with Ky Fan 2-k-norm

We propose Ky Fan 2-k-norm-based models for the non-convex low-rank matrix recovery problem. A general difference of convex algorithm (DCA) is developed to solve these models. Numerical results show that the proposed models achieve high recoverability rates

Robust newsvendor games with ambiguity in demand distributions

In classical newsvendor games, vendors collaborate to serve their aggregate demand whose joint distribution is assumed known with certainty. We investigate a new class of newsvendor games with ambiguity in the joint demand distributions, which is represented by a Fréchet class of distributions with some, possibly overlapping, marginal information. To model this new class of games, we use ideas from distributionally robust optimization to handle distributional ambiguity and study the robust newsvendor games. We provide conditions for the existence of core solutions of these games using the structural analysis of the worst-case joint demand distributions of the corresponding distributionally robust newsvendor optimization problem

Robustness to dependency in portfolio optimization using overlapping marginals

In this paper, we develop a distributionally robust portfolio optimization model where the robustness is across different dependency structures among the random losses. For a Fr´echet class of discrete distributions with overlapping marginals, we show that the distributionally robust portfolio optimization problem is efficiently solvable with linear programming. To guarantee the existence of a joint multivariate distribution consistent with the overlapping marginal information, we make use of a graph theoretic property known as the running intersection property. Building on this property, we develop a tight linear programming formulation to find the optimal portfolio that minimizes the worst-case Conditional Value-at-Risk measure. Lastly, we use a data-driven approach with financial return data to identify the Fr´echet class of distributions satisfying the running intersection property and then optimize the portfolio over this class of distributions. Numerical results in two different datasets show that the distributionally robust portfolio optimization model improves on the sample-based approac