Related papers: Inverse Mixed Integer Optimization: An Interior Po…
We study inverse optimization (IO), where the goal is to use a parametric optimization program as the hypothesis class to infer relationships between input-decision pairs. Most of the literature focuses on learning only the objective…
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…
Quantum relative entropy optimization refers to a class of convex problems in which a linear functional is minimized over an affine section of the epigraph of the quantum relative entropy function. Recently, the self-concordance of a…
Inventory management, vehicle routing, and delivery scheduling decisions are simultaneously considered in the context of the inventory routing problem. This paper focuses on the continuous-time version of this problem where, unlike its more…
This paper discusses an outer-approximation guided optimization method for constrained neural network inverse problems with rectified linear units. The constrained neural network inverse problems refer to an optimization problem to find the…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
In this paper, we consider the canonical water network design problem, which contains nonconvex potential loss functions and discrete resistance choices with varying costs. Traditionally, to resolve the nonconvexities of this problem,…
We present a two-level branch-and-bound (BB) algorithm to compute the optimal gripper pose that maximizes a grasp metric in a restricted search space. Our method can take the gripper's kinematics feasibility into consideration to ensure…
Interior-point methods for linear programming problems require the repeated solution of a linear system of equations. Solving these linear systems is non-trivial due to the severe ill-conditioning of the matrices towards convergence. This…
We present an algorithm to perform trust-region-based optimization for nonlinear unconstrained problems. The method selectively uses function and gradient evaluations at different floating-point precisions to reduce the overall energy…
$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
Bayesian optimization methods have been successfully applied to black box optimization problems that are expensive to evaluate. In this paper, we adapt the so-called super effcient global optimization algorithm to solve more accurately…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
Mixed Integer Programming (MIP) is one of the most widely used modeling techniques for combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model…
Several novel mixed-integer linear and bilinear formulations are proposed for the optimum communication spanning tree problem. They implement the distance-based approach: graph distances are directly modeled by continuous, integral, or…
We consider primal-dual pairs of semidefinite programs and assume that they are ill-posed, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such circumstances, strong duality may break down and the primal…
We present a finitely convergent cutting-plane algorithm for solving a general mixed-integer convex program given an oracle for solving a general convex program. This method is extended to solve a family of two-stage mixed-integer convex…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…