Related papers: Mixed-integer linearity in nonlinear optimization:…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
In this work, we present an algorithmically tractable safe approximation of distributionally robust optimization (DRO) problems that contain univariate indicator functions. The latter appear in different applications, but render the model…
We consider optimal control problems with integer-valued controls and a total variation regularization penalty in the objective on domains of dimension two or higher. The penalty yields that the feasible set is sequentially closed in the…
We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…
This work addresses the problem of risk-sensitive control for nonlinear systems with imperfect state observations, extending results for the linear case. In particular, we derive an algorithm that can compute local solutions with…
The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the minimal number of inequalities needed to formulate a linear optimization problem over X without using auxiliary variables. Besides its relevance…
Decision trees usefully represent sparse, high dimensional and noisy data. Having learned a function from this data, we may want to thereafter integrate the function into a larger decision-making problem, e.g., for picking the best chemical…
Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a current iterate is augmented to a better solution or proved optimal. It is well known that the performance of these methods, i.e.,…
We present a new framework for the solution of mathematical programs with equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is viewed as a concentration of an unconstrained optimization which minimizes the…
The parallel solution of large scale non-linear programming problems, which arise for example from the discretization of non-linear partial differential equations, is a highly demanding task. Here, a novel solution strategy is presented,…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
This paper presents a mixed-integer quadratic programming formulation of an existing data-driven approach to computational elasticity. This formulation is suitable for application of a standard mixed-integer programming solver, which finds…
Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…
This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…
This paper deals with a distributed Mixed-Integer Linear Programming (MILP) set-up arising in several control applications. Agents of a network aim to minimize the sum of local linear cost functions subject to both individual constraints…
This paper investigates energy-minimization finite-element approaches for the computation of nematic liquid crystal equilibrium configurations. We compare the performance of these methods when the necessary unit-length constraint is…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
We study the integrality gap of convex mixed-integer programs, that is, the difference between the optimal value of such a problem and the optimal value of its continuous relaxation. We study classes of convex sets whose associated…