Related papers: Solving Large-Scale Optimization Problems Related …
Interior point methods are among the most popular techniques for large scale nonlinear optimization, owing to their intrinsic ability of scaling to arbitrary large problem sizes. Their efficiency has attracted in recent years a lot of…
This paper proposes an interior-point framework for constrained optimization problems whose decision variables evolve on matrix Lie groups. The proposed method, termed the Matrix Lie Group Interior-Point Method (MLG-IPM), operates directly…
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…
This paper considers a class of convex optimization problems where both, the objective function and the constraints, have a continuously varying dependence on time. Our goal is to develop an algorithm to track the optimal solution as it…
In this paper we present a novel numerical method for computing local minimizers of twice smooth differentiable non-linear programming (NLP) problems. So far all algorithms for NLP are based on either of the following three principles:…
Classical control of cyber-physical systems used to rely on basic linear controllers. These controllers provided a safe and robust behavior but lack the ability to perform more complex controls such as aggressive maneuvering or performing…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
The demand for classical-quantum hybrid algorithms to solve large-scale combinatorial optimization problems using quantum annealing (QA) has increased. One approach involves obtaining an approximate solution using classical algorithms and…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
This paper takes an empirical look at asymptotic runtime growth rates for the most widely used algorithms for solving linear programming (LP) problems across a set of six optimization application areas that are known to produce large and…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
This paper presents a quantum-enhanced optimization approach for solving optimal power flow (OPF) by integrating the interior point method (IPM) with a coherent variational quantum linear solver (CVQLS). The objective is to explore the…
The advent of efficient interior point optimization methods has enabled the tractable solution of large-scale linear and nonlinear programming (NLP) problems. A prominent example of such a method is seen in Ipopt, a widely-used, open-source…
Discrete Optimal Transport problems give rise to very large linear programs (LP) with a particular structure of the constraint matrix. In this paper we present a hybrid algorithm that mixes an interior point method (IPM) and column…
We consider a class of optimization problems for sparse signal reconstruction which arise in the field of Compressed Sensing (CS). A plethora of approaches and solvers exist for such problems, for example GPSR, FPC AS, SPGL1, NestA,…
The correlations of certain entangled quantum states can be fully reproduced via a local model. We discuss in detail the practical implementation of an algorithm for constructing local models for entangled states, recently introduced by…
Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
Bell's seminal work showed that no local hidden variable (LHV) model can fully reproduce the quantum correlations of a two-qubit singlet state. His argument and later developments by Clauser et al. effectively rely on gaps between the…