Related papers: Relaxation methods for pessimistic bilevel optimiz…
The most common procedure to solve a linear bilevel problem in the PES community is, by far, to transform it into an equivalent single-level problem by replacing the lower level with its KKT optimality conditions. Then, the complementarity…
We develop tractable convex relaxations for rank-constrained quadratic optimization problems over $n \times m$ matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral…
In this paper we propose a generalized condition for a sharp minimum, somewhat similar to the inexact oracle proposed recently by Devolder-Glineur-Nesterov. The proposed approach makes it possible to extend the class of applicability of…
We propose a bilevel optimization strategy for selecting the best hyperparameter value for the nonsmooth $\ell_p$ regularizer with $0<p\le 1$. The concerned bilevel optimization problem has a nonsmooth, possibly nonconvex,…
We investigate an alternative solution method to the joint signal-beamformer optimization problem considered by Setlur and Rangaswamy[1]. First, we directly demonstrate that the problem, which minimizes the received noise, interference, and…
Most existing work focuses on the generalization of KKT for nonsmooth convex optimization problems, but this paper explores a generalized form of Karush-Kuhn-Tucker (KKT) conditions for real continuous optimization problems.
We extend in two ways the standard Karush-Kuhn-Tucker optimality conditions to problems with a convex objective, convex functional constraints, and the extra requirement that some of the variables must be integral. While the standard…
Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain…
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 these convex hulls to obtain strong yet computationally…
This paper is devoted to studying the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into a single-level optimization problem by means of the lower-level optimal value function reformulation.…
The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact…
Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…
Constrained bilevel optimization tackles nested structures present in constrained learning tasks like constrained meta-learning, adversarial learning, and distributed bilevel optimization. However, existing bilevel optimization methods…
In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the…
Linear bilevel programs (linear BLPs) have been widely used in computational mathematics and optimization in several applications. Single-level reformulation for linear BLPs replaces the lower-level linear program with its…
This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…
This paper presents an efficient parallel Cholesky factorization and triangular solve algorithm for the Karush-Kuhn-Tucker (KKT) systems arising in multistage optimization problems, with a focus on model predictive control and trajectory…
We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation).…