Related papers: Efficient Interior-Point Methods for Hyperbolic Pr…

We propose a novel methodology for solving a two-stage adjustable robust convex optimisation problem with a general (proximable) convex objective function and constraints defined by sum-of-squares (SOS) convex polynomials. These problems…

The rapid progress in GPU computing has revolutionized many fields, yet its potential in mathematical programming, such as linear programming (LP), has only recently begun to be realized. This survey aims to provide a comprehensive overview…

Second-order Newton-type algorithms that leverage the exact Hessian or its approximation are central to solve nonlinear optimization problems. However, their applications in solving large-scale nonconvex problems are hindered by three…

We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve SDPs work in the space of positive semidefinite matrices. Contrary to that the proposed…

We present differentially private (DP) algorithms for bilevel optimization, a problem class that received significant attention lately in various machine learning applications. These are the first algorithms for such problems under standard…

We introduce a two-level direct solver for the Hierarchical Poincar\'e-Steklov (HPS) method for solving linear elliptic PDEs. HPS combines multidomain spectral collocation with a direct solver, enabling high-order discretizations for highly…

Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian…

We propose a fast second-order method that can be used as a drop-in replacement for current deep learning solvers. Compared to stochastic gradient descent (SGD), it only requires two additional forward-mode automatic differentiation…

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…

While interior point methods have been the centerpiece of nonlinear programming tools used in science and engineering, their reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it…

Semidefinite programming (SDP) relaxation has emerged as a promising approach for neural network verification, offering tighter bounds than other convex relaxation methods for deep neural networks (DNNs) with ReLU activations. However, we…

We introduce a novel method for handling endpoint constraints in constrained differential dynamic programming (DDP). Unlike existing approaches, our method guarantees quadratic convergence and is exact, effectively managing rank…

Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

We have developed a new embedding method for solving scalar hyperbolic conservation laws on surfaces. The approach represents the interface implicitly by a signed distance function following the typical level set method and some embedding…

We propose a new deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and forward-backward stochastic differential equations with jumps (FBSDEJs). This novel algorithm can be viewed as an…

In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in [An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming, Computational Optimization and Applications, 78,…

Differential Dynamic Programming (DDP) is one of the indirect methods for solving an optimal control problem. Several extensions to DDP have been proposed to add stagewise state and control constraints, which can mainly be classified as…

In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…

We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and…