Related papers: Robust two-stage combinatorial optimization proble…
This paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 Wasserstein balls. We present optimality conditions for the dual of the worst-case expectation problem, which…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
In bilevel and robust optimization we are concerned with combinatorial min-max problems, for example from the areas of min-max regret robust optimization, network interdiction, most vital vertex problems, blocker problems, and two-stage…
We consider a two-stage stochastic optimization problem, in which a long-term optimization variable is coupled with a set of short-term optimization variables in both objective and constraint functions. Despite that two-stage stochastic…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…
Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…
This paper addresses the transmission network expansion planning problem considering storage units under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby short- and long-term…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
This work studies equilibrium problems under uncertainty where firms maximize their profits in a robust way when selling their output. Robust optimization plays an increasingly important role when best guaranteed objective values are to be…
We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…
We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
We examine a constrained Markov decision process under uncertain transition probabilities, with the uncertainty modeled as deviations from observed transition probabilities. We construct the uncertainty set associated with the deviations…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…
We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and…
We propose a novel methodology for solving a two-stage adjustable robust convex optimisation problem with a general (proximable) convex objective function and constraints defined by sum-of-squares (SOS) convex polynomials. These problems…