[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 …
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
We consider solving high-order and tight semidefinite programming (SDP) relaxations of
nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one …
nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one …
Ideal formulations for constrained convex optimization problems with indicator variables
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 …
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 …
quadratic objective over a nonconvex quadratic constraint. A lifting of this problem recasts …
Neuro-symbolic learning yielding logical constraints
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 …
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
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 …
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
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 …
recovers a given set of observations as accurately as possible. Unfortunately, existing …
A new perspective on low-rank optimization
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 …
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
Motivated by modern regression applications, in this paper, we study the convexification of
quadratic optimization problems with indicator variables and combinatorial constraints on …
quadratic optimization problems with indicator variables and combinatorial constraints on …
The convex hull of a quadratic constraint over a polytope
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 …
the objective function is a quadratic function and the feasible region is defined by quadratic …