Related papers: A Polyhedral Study on Unit Commitment with a Singl…

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…

The presence of symmetries of binary programs typically degrade the performance of branch-and-bound solvers. In this article, we derive efficient variable fixing algorithms to discard symmetric solutions from the search space based on…

We develop a data-driven approach to the computation of a-posteriori feasibility certificates to the solution sets of variational inequalities affected by uncertainty. Specifically, we focus on instances of variational inequalities with a…

Being cautious is crucial for enhancing the trustworthiness of machine learning systems integrated into decision-making pipelines. Although calibrated probabilities help in optimal decision-making, perfect calibration remains unattainable,…

We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depends on the uncertainty parameter. The interest of our…

Complex system design problems, such as those involved in aerospace engineering, require the use of numerically costly simulation codes in order to predict the performance of the system to be designed. In this context, these codes are often…

As net-load becomes less predictable there is a lot of pressure in changing decision models for power markets such that they account explicitly for future scenarios in making commitment decisions. This paper proposes to make commitment…

We propose a novel global solution algorithm for the network-constrained unit commitment problem incorporating a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming…

We study the problem of minimizing a multivariate polynomial function over the unit hypercube. By representing the polynomial through a hypergraph and exploiting its sparsity structure, we establish a new sufficient condition under which…

As renewable wind energy penetration rates continue to increase, one of the major challenges facing grid operators is the question of how to control transmission grids in a reliable and a cost-efficient manner. The stochastic nature of wind…

This work proposes a framework for multistage adjustable robust optimization that unifies the treatment of three different types of endogenous uncertainty, where decisions, respectively, (i) alter the uncertainty set, (ii) affect the…

When modeling energy storage systems, an essential question is how to account for the physical infeasibility of simultaneous charge and discharge. The use of complementarity constraints or of binary variables is common, but these…

We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…

Distributionally robust optimization is used to tackle decision making problems under uncertainty where the distribution of the uncertain data is ambiguous. Many ambiguity sets have been proposed for continuous uncertainty that build on…

A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…

Constructing uncertainty sets as unions of multiple subsets has emerged as an effective approach for creating compact and flexible uncertainty representations in data-driven robust optimization (RO). This paper focuses on two separate…

Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…

We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…

Linearly constrained multiple time series may be encountered in many practical contexts, such as the National Accounts (e.g., GDP disaggregated by Income, Expenditure and Output), and multilevel frameworks where the variables are organized…

In robust optimization one seeks to make a decision under uncertainty, where the goal is to find the solution with the best worst-case performance. The set of possible realizations of the uncertain data is described by a so-called…