Related papers: A Polyhedral Study on Unit Commitment with a Singl…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
In this paper we present a formulation of the unit commitment problem with AC power flow constraints. It is solved by a Benders decomposition in which the unit commitment master problem is formulated as a mixed-integer problem with…
The blast wave of machine learning and artificial intelligence has also reached the power systems community, and amid the frenzy of methods and black-box tools that have been left in its wake, it is sometimes difficult to perceive a glimmer…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…
We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-e reliability criterion. This reliability criterion is a generalization of the…
We are interested in finding a family of solutions to a singularly perturbed biharmonic equation which has a concentration behavior. The proof is based on variational methods and it is used a weak version of the Ambrosetti-Rabinowitz…
We study the mixed-integer quadratic programming formulation of an $n$-period hybrid control problem with a convex quadratic cost function and linear dynamics. We first give the convex hull description of the single-period, two-mode problem…
Power company operators make power generation plans one day in advance, in what is known as the Unit Commitment (UC) problem. UC is exposed to uncertainties, such as unknown electricity load and disturbances caused by renewable energy…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
Constraint-solving-based program invariant synthesis takes a parametric invariant template and encodes the (inductive) invariant conditions into constraints. The problem of characterizing the set of all valid parameter assignments is…
The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we…
This paper proposes a unit commitment (UC) model based on data-driven Wasserstein distributionally robust optimization (WDRO) for power systems under uncertainty of renewable generation as well as its tractable exact reformulation. The…
This paper studies, for the first time, a bilevel polynomial program whose constraints involve uncertain linear constraints and another uncertain linear optimization problem. In the case of box data uncertainty, we present a sum of squares…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
The quantum hybrid algorithm has become a very promising and speedily method today for solving the larger-scale optimization in the noisy intermediate-scale quantum (NISQ) era. The unit commitment (UC) problem is a fundamental problem in…
From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network. Our formulation requires a single binary variable and no additional continuous variables beyond the…