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Robust PCA has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bio-informatics, statistics, and machine learning to image and video processing in computer vision. Robust PCA…
Classification, recommendation, and ranking problems often involve competing goals with additional constraints (e.g., to satisfy fairness or diversity criteria). Such optimization problems are quite challenging, often involving non-convex…
Quadratic Unconstrained Binary Optimization (QUBO) problems are prevalent in various applications and are known to be NP-hard. The seminal work of Goemans and Williamson introduced a semidefinite programming (SDP) relaxation for such…
We study the design of computationally efficient algorithms with provable guarantees, that are robust to adversarial (test time) perturbations. While there has been an proliferation of recent work on this topic due to its connections to…
We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance…
A popular approach for addressing uncertainty in variational inequality problems is by solving the expected residual minimization (ERM) problem. This avenue necessitates distributional information associated with the uncertainty and…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…
We provide necessary and sufficient conditions for robust efficiency (in the sense of Ehrgott et al. (2014)) to multiobjective optimization problems that depend on uncertain parameters. These conditions state that a solution is robust…
From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…
Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…
Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ and a feasible set…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
One of the arduous tasks in supply chain modelling is to build robust models against irregular variations. During the proliferation of time-series analyses and machine learning models, several modifications were proposed such as…
Pareto-optimality plays a central role in evaluating the efficiency of solutions to allocation problems, such as house allocation, school choice, and kidney exchange. We introduce a general linear programming problem subject to…
We consider large-scale Markov decision processes (MDPs) with parameter uncertainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handle uncertainty, can be solved using dynamic…