[HTML][HTML] (Global) optimization: historical notes and recent developments

M Locatelli, F Schoen - EURO Journal on Computational Optimization, 2021 - Elsevier
Abstract Recent developments in (Global) Optimization are surveyed in this paper. We
collected and commented quite a large number of recent references which, in our opinion …

An inexact projected gradient method with rounding and lifting by nonlinear programming for solving rank-one semidefinite relaxation of polynomial optimization

H Yang, L Liang, L Carlone, KC Toh - Mathematical Programming, 2023 - Springer
We consider solving high-order and tight semidefinite programming (SDP) relaxations of
nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one …

Ideal formulations for constrained convex optimization problems with indicator variables

L Wei, A Gómez, S Küçükyavuz - Mathematical Programming, 2022 - Springer
Motivated by modern regression applications, in this paper, we study the convexification of a
class of convex optimization problems with indicator variables and combinatorial constraints …

The generalized trust region subproblem: solution complexity and convex hull results

AL Wang, F Kılınç-Karzan - Mathematical Programming, 2022 - Springer
We consider the generalized trust region subproblem (GTRS) of minimizing a nonconvex
quadratic objective over a nonconvex quadratic constraint. A lifting of this problem recasts …

Neuro-symbolic learning yielding logical constraints

Z Li, Y Huang, Z Li, Y Yao, J Xu… - Advances in Neural …, 2024 - proceedings.neurips.cc
Neuro-symbolic systems combine the abilities of neural perception and logical reasoning.
However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This …

Exactness of Parrilo's conic approximations for copositive matrices and associated low order bounds for the stability number of a graph

M Laurent, LF Vargas - Mathematics of Operations …, 2023 - pubsonline.informs.org
De Klerk and Pasechnik introduced in 2002 semidefinite bounds ϑ (r)(G)(r≥ 0) for the
stability number α (G) of a graph G and conjectured their exactness at order r= α (G)− 1 …

Optimal low-rank matrix completion: Semidefinite relaxations and eigenvector disjunctions

D Bertsimas, R Cory-Wright, S Lo… - arXiv preprint arXiv …, 2023 - arxiv.org
Low-rank matrix completion consists of computing a matrix of minimal complexity that
recovers a given set of observations as accurately as possible. Unfortunately, existing …

A new perspective on low-rank optimization

D Bertsimas, R Cory-Wright, J Pauphilet - Mathematical Programming, 2023 - Springer
A key question in many low-rank problems throughout optimization, machine learning, and
statistics is to characterize the convex hulls of simple low-rank sets and judiciously apply …

On the convexification of constrained quadratic optimization problems with indicator variables

L Wei, A Gómez, S Küçükyavuz - International conference on integer …, 2020 - Springer
Motivated by modern regression applications, in this paper, we study the convexification of
quadratic optimization problems with indicator variables and combinatorial constraints on …

The convex hull of a quadratic constraint over a polytope

A Santana, SS Dey - SIAM Journal on Optimization, 2020 - SIAM
A quadratically constrained quadratic program (QCQP) is an optimization problem in which
the objective function is a quadratic function and the feasible region is defined by quadratic …