Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization

1996 ◽  
Vol 75 (3) ◽  
pp. 377-397 ◽  
Author(s):  
Hiroshi Yamashita ◽  
Hiroshi Yabe
Keyword(s):  
Constrained Optimization ◽  
Interior Point ◽  
Quadratic Convergence ◽  
Interior Point Methods ◽  
Primal Dual

Correlative Sparsity in Primal-Dual Interior-Point Methods for LP, SDP, and SOCP

2007 ◽  
Vol 58 (1) ◽  
pp. 69-88 ◽  
Author(s):  
Kazuhiro Kobayashi ◽  
Sunyoung Kim ◽  
Masakazu Kojima
Keyword(s):  
Interior Point ◽  
Interior Point Methods ◽  
Primal Dual

AN INTERIOR POINT APPROACH FOR SEMIDEFINITE OPTIMIZATION USING NEW PROXIMITY FUNCTIONS

2009 ◽  
Vol 26 (03) ◽  
pp. 365-382 ◽  
Author(s):  
M. REZA PEYGHAMI
Keyword(s):  
Interior Point ◽  
Interior Point Methods ◽  
Linear Optimization ◽  
Kernel Functions ◽  
Semidefinite Optimization ◽  
Special Choice ◽  
Simple Analysis ◽  
New Class ◽  
Iteration Bound ◽  
Primal Dual

Kernel functions play an important role in interior point methods (IPMs) for solving linear optimization (LO) problems to define a new search direction. In this paper, we consider primal-dual algorithms for solving Semidefinite Optimization (SDO) problems based on a new class of kernel functions defined on the positive definite cone [Formula: see text]. Using some appealing and mild conditions of the new class, we prove with simple analysis that the new class-based large-update primal-dual IPMs enjoy an [Formula: see text] iteration bound to solve SDO problems with special choice of the parameters of the new class.

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