Related papers: OSQP: An Operator Splitting Solver for Quadratic P…
This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems…
Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables.…
We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…
We present a globally convergent SQP-type method with the least constraint violation for nonlinear semidefinite programming. The proposed algorithm employs a two-phase strategy coupled with a line search technique. In the first phase, a…
The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold…
Quadratic programming (QP) is a fundamental optimization model with wide-ranging applications in decision-making and machine learning, yet efficiently solving large-scale instances remains a major computational challenge. Building upon the…
Integer Quadratic Programming (IQP) is an important problem in operations research. Local search is a powerful method for solving hard problems, but the research on local search algorithms for IQP solving is still on its early stage. This…
We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…
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…
Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…
For a specific quantum chip, multi-programming helps to improve overall throughput and resource utilization. However, the previous solutions for mapping multiple programs onto a quantum chip often lead to resource under-utilization, high…
We present a finitely convergent cutting-plane algorithm for solving a general mixed-integer convex program given an oracle for solving a general convex program. This method is extended to solve a family of two-stage mixed-integer convex…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Quadratic cone programs are rapidly becoming the standard canonical form for convex optimization problems. In this paper we address the question of differentiating the solution map for such problems, generalizing previous work for linear…
Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…
Semidefinite programming (SDP) is a fundamental convex optimization problem with wide-ranging applications. However, solving large-scale instances remains computationally challenging due to the high cost of solving linear systems and…
Small-scale Mixed-Integer Quadratic Programming (MIQP) problems often arise in embedded control and estimation applications. Driven by the need for algorithmic simplicity to target computing platforms with limited memory and computing…