Complementarity problems over symmetric cones: a survey of recent developments in several aspects

A Yoshise - Handbook on Semidefinite, Conic and Polynomial …, 2012 - Springer
The complementarity problem over a symmetric conic (that we call the Symmetric Conic
Complementarity Problem, or the SCCP) has received much attention of researchers in the …

A new interior-point algorithm based on modified Nesterov–Todd direction for symmetric cone linear complementarity problem

B Kheirfam, N Mahdavi-Amiri - Optimization Letters, 2014 - Springer
We present a new primal-dual path-following interior-point algorithm for linear
complementarity problem over symmetric cones. The algorithm is based on a reformulation …

Clarabel: An interior-point solver for conic programs with quadratic objectives

PJ Goulart, Y Chen - arXiv preprint arXiv:2405.12762, 2024 - arxiv.org
We present a general-purpose interior-point solver for convex optimization problems with
conic constraints. Our method is based on a homogeneous embedding method originally …

Kernel-based interior-point methods for monotone linear complementarity problems over symmetric cones

G Lesaja, C Roos - Journal of optimization theory and applications, 2011 - Springer
We present an interior-point method for monotone linear complementarity problems over
symmetric cones (SCLCP) that is based on barrier functions which are defined by a large …

Pseudomonotonicity of Nonlinear Transformations on Euclidean Jordan Algebras

YM Li - Acta Mathematicae Applicatae Sinica, English Series, 2024 - Springer
In this paper, we have introduced the concepts of pseudomonotonicity properties for
nonlinear transformations defined on Euclidean Jordan algebras. The implications between …

An interior-point method for the Cartesian P*(Κ)-linear complementarity problem over symmetric cones

B Kheirfam - ORiON, 2014 - journals.co.za
A novel primal-dual path-following interior-point algorithm for the Cartesian P*(Κ)-linear
complementarity problem over symmetric cones is presented. The algorithm is based on a …

[PDF][PDF] Several developments of variational inequalities and complementarity problems, bilevel programming and MPEC

Z HUANG, G LIN, N XIU - Operations Research, 2014 - aim.shu.edu.cn
This paper investigates finite-dimensional variational inequalities and complementarity
problems, bilevel programming problems and mathematical programs with equilibrium …

变分不等式与互补问题, 双层规划与平衡约束数学规划问题的若干进展

黄正海, 林贵华, 修乃华 - 运筹学学报, 2014 - ort.shu.edu.cn
考虑有限维变分不等式与互补问题, 双层规划以及均衡约束的数学规划问题.
在简单介绍这些问题之后, 重点介绍近年来这些领域中发展迅速的几个研究方向 …

A generic interior-point algorithm for monotone symmetric cone linear complementarity problems based on a new kernel function

B Kheirfam - Journal of Mathematical Modelling and Algorithms in …, 2014 - Springer
Kernel functions play an important role in defining new search directions for interior-point
algorithms for solving monotone linear complementarity problems. In this paper we present …

Efficient numerical algorithms for large-scale conic optimization

Y Chen - 2024 - ora.ox.ac.uk
Conic optimization has been widely used in many areas, such as machine learning, image
processing and automatic control. It usually relies on iterative algorithms to find the optimum …