# Self-regular functions and new search directions for linear and semidefinite optimization

@article{Peng2002SelfregularFA,
title={Self-regular functions and new search directions for linear and semidefinite optimization},
author={Jiming Peng and Kees Roos and Tam{\'a}s Terlaky},
journal={Mathematical Programming},
year={2002},
volume={93},
pages={129-171}
}
• Published 2002
• Mathematics, Computer Science
• Mathematical Programming
Abstract.In this paper, we introduce the notion of a self-regular function. Such a function is strongly convex and smooth coercive on its domain, the positive real axis. We show that any such function induces a so-called self-regular proximity function and a corresponding search direction for primal-dual path-following interior-point methods (IPMs) for solving linear optimization (LO) problems. It is proved that the new large-update IPMs enjoy a polynomial ?(n$\frac{q+1}{2q}$log$\frac{n… Expand 212 Citations #### Topics from this paper A large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function AbstractIn this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. ItExpand A new primal-dual interior-point method for semidefinite optimization based on a parameterized kernel function • Mathematics • 2020 As indicated in the recent studies about primal-dual interior-point methods (IPMs) based on kernel functions, a kernel function not only serves to determine the search direction and measure theExpand Primal-Dual Interior-Point Algorithms for Semidefinite Optimization Based on a Simple Kernel Function • Mathematics, Computer Science • J. Math. Model. Algorithms • 2005 This paper presents a primal-dual interior-point algorithm for SDO problems based on a simple kernel function which was first presented at the Proceedings of Industrial Symposium and Optimization Day, Australia, November 2002; the function is not self-regular. Expand An interior Point Approach for Semidefinite Optimization Using New Proximity Functions • M. Peyghami • Mathematics, Computer Science • Asia Pac. J. Oper. Res. • 2009 It is proved with simple analysis that the new class-based large-update primal-dual IPMs enjoy an iteration bound to solve Semidefinite Optimization (SDO) problems with special choice of the parameters of the newclass. Expand New parameterized kernel functions for linear optimization • Mathematics, Computer Science • J. Glob. Optim. • 2012 A new class of parameterized kernel functions is proposed for the development of primal-dual interior-point algorithms for solving linear programming problems and leads to a complexity bounds of O(\sqrt{n}\,{\rm log}\,n\,log}\,\frac{n}{\epsilon}\right)} for the large-update primal- dual interior point methods. Expand A Comparative Study of Kernel Functions for Primal-Dual Interior-Point Algorithms in Linear Optimization • Mathematics, Computer Science • SIAM J. Optim. • 2004 It is shown that small-update methods based on the new kernel functions all have the same complexity as the classical primal-dual IPM, namely,$O(\sqrt{n}(\log n)\log\frac{n}{\e})\$. Expand
Complexity analysis of an interior point algorithm for the semidefinite optimization based on a kernel function with a double barrier term
AbstractIn this paper, we establish the polynomial complexity of a primal-dual path-following interior point algorithm for solving semidefinite optimization (SDO) problems. The proposed algorithm isExpand
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In this paper we present a class of polynomial primal-dual interior-point algorithms for linear optimization based on a new class of kernel functions. This class is fairly general and includes theExpand
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• Mathematics
• 2008
In this paper we present a class of polynomial primal-dual interior-point algorithms for linear optimization based on a new class of kernel functions. This class is fairly general and includes theExpand
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