Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms Book

	Preface
	Acknowledgements
	Notation
	List of Abbreviations
Ch. 1	Introduction and Preliminaries	1
1.1	Historical Background of Interior-Point Methods	2
1.2	Primal-Dual Path-Following Algorithm for LO	5
1.3	Preliminaries and Scope of the Monograph	16
Ch. 2	Self-Regular Functions and Their Properties	27
2.1	An Introduction to Univariate Self-Regular Functions	28
2.2	Basic Properties of Univariate Self-Regular Functions	35
2.3	Relations Between S-R and S-C Functions	42
Ch. 3	Primal-Dual Algorithms for Linear Optimization Based on Self-Regular Proximities	47
3.1	Self-Regular Functions in [actual symbol not reproducible] and Self-Regular Proximities for LO	48
3.2	The Algorithm	52
3.3	Estimate of the Proximity After a Newton Step	55
3.4	Complexity of the Algorithm	61
3.5	Relaxing the Requirement on the Proximity Function	63
Ch. 4	Interior-Point Methods for Complementarity Problems Based on Self-Regular Proximities	67
4.1	Introduction to CPs and the Central Path	68
4.2	Preliminary Results on [actual symbol not reproducible] Mappings	72
4.3	New Search Directions for [actual symbol not reproducible] CPs	80
4.4	Complexity of the Algorithm	83
Ch. 5	Primal-Dual Interior-Point Methods for Semidefinite Optimization Based on Self-Regular Proximities	99
5.1	Introduction to SDO, Duality Theory and Central Path	100
5.2	Preliminary Results on Matrix Functions	103
5.3	New Search Directions for SDO	111
5.4	New Polynomial Primal-Dual IPMs for SDO	117
Ch. 6	Primal-Dual Interior-Point Methods for Second-Order Conic Optimization Based on Self-Regular Proximities	125
6.1	Introduction to SOCO, Duality Theory and The Cental Path	126
6.2	Preliminary Results on Functions Associated with Second-Order Cones	129
6.3	New Search Directions for SOCO	142
6.4	New IPMs for SOCO	150
Ch. 7	Initialization: Embedding Models for Linear Optimization, Complementarity Problems, Semidefinite Optimization and Second-Order Conic Optimization	159
7.1	The Self-Dual Embedding Model for LO	160
7.2	The Embedding Model for CP	162
7.3	Self-Dual Embedding Models for SDO and SOCO	165
Ch. 8	Conclusions	169
8.1	A Survey of the Results and Future Research Topics	170
	References	175
	Index	183