Related papers: An asymptotically superlinearly convergent semismo…

This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…

Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are…

Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs…

Embedding deep neural networks (NNs) into mixed-integer programs (MIPs) is attractive for decision making with learned constraints, yet state-of-the-art monolithic linearisations blow up in size and quickly become intractable. In this…

Image restoration is typically addressed through non-convex inverse problems, which are often solved using first-order block-wise splitting methods. In this paper, we consider a general type of non-convex optimisation model that captures…

The operation of large-scale infrastructure networks requires scalable optimization schemes. To guarantee safe system operation, a high degree of feasibility in a small number of iterations is important. Decomposition schemes can help to…

In large-scale optimization, when either forming or storing Hessian matrices are prohibitively expensive, quasi-Newton methods are often used in lieu of Newton's method because they only require first-order information to approximate the…

Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks, but their deployment is often constrained by substantial memory footprints and computational costs. While prior work has achieved…

In this paper, we consider finding a low-rank approximation to the solution of a large-scale generalized Lyapunov matrix equation in the form of $A X M + M X A = C$, where $A$ and $M$ are symmetric positive definite matrices. An algorithm…

Iterative Refinement (IR) is a classical computing technique for obtaining highly precise solutions to linear systems of equations, as well as linear optimization problems. In this paper, motivated by the limited precision of quantum…

The work of Wachter and Biegler suggests that infeasible-start interior point methods (IPMs) developed for linear programming cannot be adapted to nonlinear optimization without significant modification, i.e., using a two-phase or penalty…

Policy iteration and value iteration are at the core of many (approximate) dynamic programming methods. For Markov Decision Processes with finite state and action spaces, we show that they are instances of semismooth Newton-type methods to…

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…

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…

An inexact semismooth Newton method has been proposed for solving semi-linear elliptic optimal control problems in this paper. This method incorporates the generalized minimal residual (GMRES) method, a type of Krylov subspace method, to…

Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…

Large language models (LLMs) have shown remarkable in-context learning (ICL) capabilities, yet their potential for sequential decision-making remains underexplored. In this paper, we study the ICL capabilities of LLMs in sequential…

We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…

As an effective emulator of ill-conditioned power flow, continuous Newton methods (CNMs) have been extensively investigated using explicit and implicit numerical integration algorithms. Explicit CNMs are prone to non-convergence issues due…

In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…