Related papers: Approximating Multiple Robust Optimization Solutio…
We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coefficients and constraint matrix entries from given interval domains there are…
Due to critical environmental issues, the power systems have to accommodate a significant level of penetration of renewable generation which requires smart approaches to the power grid control. Associated optimal control problems are…
The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
In robust decision-making under non-Bayesian uncertainty, different robust optimization criteria, such as maximin performance, minimax regret, and maximin ratio, have been proposed. In many problems, all three criteria are well-motivated…
Robust optimization methods have shown practical advantages in a wide range of decision-making applications under uncertainty. Recently, their efficacy has been extended to multi-period settings. Current approaches model uncertainty either…
The Proximal Point Method (PPM) (Rockafellar, 1976) is a fundamental tool for nonsmooth convex optimization. However, its convergence is not linear under general convexity in the absence of strong convexity or other structural assumptions.…
Algorithms with predictions} has emerged as a powerful framework to combine the robustness of traditional online algorithms with the data-driven performance benefits of machine-learned (ML) predictions. However, most existing approaches in…
We consider global non-convex optimisation problems under uncertainty. In this setting, it is not possible to implement a desired solution exactly. Instead, any other solution within some distance to the intended solution may be…
Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become…
Model Predictive Control (MPC) is an optimal control algorithm with strong stability and robustness guarantees. Despite its popularity in robotics and industrial applications, the main challenge in deploying MPC is its high computation…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…
We treat uncertain linear programming problems by utilizing the notion of weighted analytic centers and notions from the area of multi-criteria decision making. After introducing our approach, we develop interactive cutting-plane algorithms…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…
A common challenge in real-time operations is deciding whether to re-solve an optimization problem or continue using an existing solution. While modern data platforms may collect information at high frequencies, many real-time operations…
Robust optimization (RO) tackles data uncertainty by optimizing for the worst-case scenario of an uncertain parameter and, in its basic form, is sometimes criticized for producing overly-conservative solutions. To reduce the level of…