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The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…

The ADMM-based interior point (ABIP, Lin et al. 2021) method is a hybrid algorithm that effectively combines interior point method (IPM) and first-order methods to achieve a performance boost in large-scale linear optimization. Different…

Optimization and Control · Mathematics 2024-04-09 Qi Deng , Qing Feng , Wenzhi Gao , Dongdong Ge , Bo Jiang , Yuntian Jiang , Jingsong Liu , Tianhao Liu , Chenyu Xue , Yinyu Ye , Chuwen Zhang

We propose a new framework to implement interior point method (IPM) to solve very large linear programs (LP). Traditional IPMs typically use Newton's method to approximately solve a subproblem that aims to minimize a log-barrier penalty…

Optimization and Control · Mathematics 2020-07-03 Tianyi Lin , Shiqian Ma , Yinyu Ye , Shuzhong Zhang

We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…

Optimization and Control · Mathematics 2024-03-06 Zhijian Lai , Akiko Yoshise

We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…

Quantum Physics · Physics 2023-09-13 Brandon Augustino , Giacomo Nannicini , Tamás Terlaky , Luis F. Zuluaga

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…

Optimization and Control · Mathematics 2019-07-15 Juraj Kardoš , Drosos Kourounis , Olaf Schenk

Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…

Optimization and Control · Mathematics 2024-10-22 Xi Gao , Jinxin Xiong , Akang Wang , Qihong Duan , Jiang Xue , Qingjiang Shi

The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…

The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush--Kuhn--Tucker (KKT) system at each iteration of the…

Optimization and Control · Mathematics 2022-03-23 François Pacaud , Sungho Shin , Michel Schanen , Daniel Adrian Maldonado , Mihai Anitescu

Since more than three decades, interior-point methods proved very useful for optimization, from linear over semidefinite to conic (and partly beyond non-convex) programming; despite the fact that already in the semidefinite case (even when…

Optimization and Control · Mathematics 2020-02-25 Konrad Schrempf

When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is…

Optimization and Control · Mathematics 2023-04-28 Filippo Zanetti , Jacek Gondzio

This paper presents a customized second-order cone programming (SOCP) solver tailored for embedded real-time optimization, which frequently arises in modern guidance and control (G&C) applications. The solver employs a practically efficient…

Optimization and Control · Mathematics 2026-03-12 Jae-Il Jang , Chang-Hun Lee

We study two fundamental optimization problems: (1) scaling a symmetric positive definite matrix by a positive diagonal matrix so that the resulting matrix has row and column sums equal to 1; and (2) minimizing a quadratic function subject…

Data Structures and Algorithms · Computer Science 2025-04-30 Adrian Vladu

In this paper, we study optimal experimental design problems with a broad class of smooth convex optimality criteria, including the classical A-, D- and p th mean criterion. In particular, we propose an interior point (IP) method for them…

Computation · Statistics 2012-10-16 Zhaosong Lu , Ting Kei Pong

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…

Optimization and Control · Mathematics 2023-03-22 Zeguan Wu , Mohammadhossein Mohammadisiahroudi , Brandon Augustino , Xiu Yang , Tamás Terlaky

In this paper, we introduce two parabolic target-space interior-point algorithms for solving monotone linear complementarity problems. The first algorithm is based on a universal tangent direction, which has been recently proposed for…

Optimization and Control · Mathematics 2025-07-31 Marianna E. -Nagy , Tibor Illés , Yurii Nesterov , Petra Renáta Rigó

Interior-point methods (IPMs) are a cornerstone of Euclidean convex optimization, due to their strong theoretical guarantees and practical performance. Motivated by scaling problems, recent work by Hirai and the last two authors (FOCS'23)…

Optimization and Control · Mathematics 2026-04-09 Christopher Criscitiello , Harold Nieuwboer , Michael Walter

We propose a family of search directions based on primal-dual entropy in the context of interior-point methods for linear optimization. We show that by using entropy based search directions in the predictor step of a predictor-corrector…

Optimization and Control · Mathematics 2014-10-31 Mehdi Karimi , Shen Lou , Levent Tunçel

Hyperbolic polynomials is a class of real-roots polynomials that has wide range of applications in theoretical computer science. Each hyperbolic polynomial also induces a hyperbolic cone that is of particular interest in optimization due to…

Optimization and Control · Mathematics 2023-06-14 Yichuan Deng , Zhao Song , Lichen Zhang , Ruizhe Zhang

In a recent paper, Skajaa and Ye proposed a homogeneous primal-dual interior-point method for non-symmetric conic optimization. The authors showed that their algorithm converges to $\varepsilon$-accuracy in $O(\sqrt{\nu}\log…

Optimization and Control · Mathematics 2018-06-18 Dávid Papp , Sercan Yıldız