Related papers: A note on generalized semi-infinite program boundi…
The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…
For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…
Generalized Benders decomposition (GBD) is a globally optimal algorithm for mixed integer nonlinear programming (MINLP) problems, which are NP-hard and can be widely found in the area of wireless resource allocation. The main idea of GBD is…
Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In…
In polynomial optimization problems, nonnegativity constraints are typically handled using the sum of squares condition. This can be efficiently enforced using semidefinite programming formulations, or as more recently proposed by Papp and…
Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…
Constrained clustering leverages limited domain knowledge to improve clustering performance and interpretability, but incorporating pairwise must-link and cannot-link constraints is an NP-hard challenge, making global optimization…
In this paper, we propose a novel decomposition approach for mixed-integer stochastic programming (SMIP) problems that is inspired by the combination of penalty-based Lagrangian and block Gauss-Seidel methods (PBGS). In this sense, PBGS is…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
We first show a simple but striking result in bilevel optimization: unconstrained $C^\infty$ smooth bilevel programming is as hard as general extended-real-valued lower semicontinuous minimization. We then proceed to a worst-case analysis…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
Shifted combinatorial optimization is a new nonlinear optimization framework, which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. It captures well studied and…
We consider the solution of nonlinear programs with nonlinear semidefiniteness constraints. The need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear semidefinite programs more…
Since more than three decades, interior-point methods proved very useful for optimization, from linear over semidefinite to conic (and partly beyond non-convex) programming; despite the fact that already in the semidefinite case (even when…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…