Related papers: Learning to Relax Nonconvex Quadratically Constrai…

Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unrealized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum…

The quadratic programming over one inequality quadratic constraint (QP1QC) is a very special case of quadratically constrained quadratic programming (QCQP) and attracted much attention since early 1990's. It is now understood that, under…

First-order methods for quadratic optimization such as OSQP are widely used for large-scale machine learning and embedded optimal control, where many related problems must be rapidly solved. These methods face two persistent challenges:…

Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer…

Bilevel optimization involves a hierarchical structure where one problem is nested within another, leading to complex interdependencies between levels. We propose a single-loop, tuning-free algorithm that guarantees anytime feasibility,…

In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…

In recent years there has been a collective research effort to find new formulations of reinforcement learning that are simultaneously more efficient and more amenable to analysis. This paper concerns one approach that builds on the linear…

Many physical systems have underlying safety considerations that require that the policy employed ensures the satisfaction of a set of constraints. The analytical formulation usually takes the form of a Constrained Markov Decision Process…

A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only…

Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…

We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. Within this framework, a quantum subroutine is incorporated…

In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for…

Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions…

Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…

We study the maximization of sums of heterogeneous quadratic forms over the Stiefel manifold, a nonconvex problem that arises in several modern signal processing and machine learning applications such as heteroscedastic probabilistic…

Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…

We develop a novel primal heuristic for nonconvex Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQPs). The method is built around a convex approximation that is dynamically adjusted within a feasibility-pump-style…

Physical design refers to mathematical optimization of a desired objective (e.g. strong light--matter interactions, or complete quantum state transfer) subject to the governing dynamical equations, such as Maxwell's or Schrodinger's…

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…

Approximate linear programming (ALP) and its variants have been widely applied to Markov Decision Processes (MDPs) with a large number of states. A serious limitation of ALP is that it has an intractable number of constraints, as a result…