We consider the problem of computing the optimal solution and objective of a linear program under linearly changing linear constraints. The problem studied is given by $\min c^t x \text{ s.t } Ax + \lambda Dx \leq b$ where $\lambda$ belongs to a set of predefined values $\Lambda$. Based on the information given by a … Read more
In this paper, we study the two-stage distributionally robust optimization (DRO) problem from the primal perspective. Unlike existing approaches, this perspective allows us to build a deeper and more intuitive understanding on DRO, to leverage classical and well established solution methods and to develop a general and fast decomposition algorithm (and its variants), and to … Read more
Two-stage robust optimization (two-stage RO), due to its ability to balance robustness and flexibility, has been widely used in various fields for decision-making under uncertainty. This paper proposes a multiple kernel learning (MKL)-aided column-and-constraint generation (CCG) method to address this issue in the context of data-driven decision optimization, and releases a corresponding registered Julia package, … Read more
It is well known that the performance of the classical Markowitz model for portfolio optimization is extremely sensitive to estimation errors on the expected asset returns. Robust optimization mitigates this issue. We focus on ellipsoidal uncertainty sets around a point estimate of the expected asset returns. An important issue is the choice of the parameters … Read more
This paper studies effective scenarios in Distributionally Robust Optimization (DRO) problems defined on a finite number of realizations (also called scenarios) of the uncertain parameters. Effective scenarios are critical scenarios in DRO in the sense that their removal from the support of the considered distributions alters the optimal value. Ineffective scenarios are those whose removal … Read more
We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in Subramanyam (2022). We first present a simple counterexample where the original conditions are insufficient, highlight where the original proof fails, and then provide modified conditions along with a correct proof of their validity. Finally, although … Read more
Distributionally robust optimization (DRO) studies decision problems under uncertainty where the probability distribution governing the uncertain problem parameters is itself uncertain. A key component of any DRO model is its ambiguity set, that is, a family of probability distributions consistent with any available structural or statistical information. DRO seeks decisions that perform best under the … Read more
Understanding the variation of the optimal value with respect to change in the data is an old problem of mathematical optimisation. This paper focuses on the linear problem f(λ) = min ctx such that (A+λD)x ≤ b, where λ is an unknown parameter that varies within an interval and D is a matrix modifying the … Read more
This paper considers the robust phase retrieval, which can be cast as a nonsmooth and nonconvex optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the inexact proximal linear algorithm (AdaIPL). Our contribution lies in the novel design of adaptive step sizes based on quantiles of the absolute … Read more
In the realm of robust optimization the k-adaptability approach is one promising method to derive approximate solutions for two-stage robust optimization problems. Instead of allowing all possible second-stage decisions, the k-adaptability approach aims at calculating a limited set of k such decisions already in the first-stage before the uncertainty reveals. The parameter k can be … Read more