This paper addresses the robust counterparts of optimization problems containing sums of maxima of linear functions and proposes several reformulations. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a...

We propose a new way to derive tractable robust counterparts of a linear conic optimization problem by using the theory of Beck and Ben-Tal on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new convex reformulation of the dual...

The purpose of this paper is to introduce the Gerber statistic, a robust co-movement measure for covariance matrix estimation for the purpose of portfolio construction. The Gerber statistic extends Kendall's Tau by counting the proportion of simultaneous co-movements in series when their...

Problem definition: Due to complex electrochemical reactions and physical conditions, the quality of used products (cores) is highly uncertain. The remanufacturer needs to make the acquisition decision under the quality distributional ambiguity. The perfect quality distribution of cores cannot...

Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein distributionally robust optimization (DRO), achieves this by...

The L1-median is a robust estimator of multivariate location with good statistical properties. Several algorithms for computing the L1-median are available. Problem specific algorithms can be used, but also general optimization routines. The aim is to compare different algorithms with respect to...

The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic...

We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. We explore the need for more general optimization tools, and consider the means by which constrained random portfolios may be generated. DeVroye's approach to sampling the interior of a...