A Matrix-Dilation Approach to Robust Semidefinite Programming and Its Error Bound

2010 ◽  
Vol 3 (5) ◽  
pp. 372-380 ◽  
Author(s):  
Yasuaki OISHI
Keyword(s):  
Semidefinite Programming ◽  
Error Bound ◽  
Matrix Dilation

scholarly journals Exploiting Sparsity in a Matrix-Dilation Approach to Robust Semidefinite Programming

2007 ◽  
Vol 43 (2) ◽  
pp. 93-101 ◽  
Author(s):  
Yusuke ISAKA ◽  
Yasuaki OISHI
Keyword(s):  
Semidefinite Programming ◽  
Matrix Dilation

scholarly journals Critical Multipliers in Semidefinite Programming

2020 ◽  
Vol 37 (04) ◽  
pp. 2040012
Author(s):  
Tianyu Zhang ◽  
Liwei Zhang
Keyword(s):  
Nonlinear Programming ◽  
Semidefinite Programming ◽  
Programming Problem ◽  
Error Bound ◽  
Variational Problems ◽  
Nonlinear Programming Problem ◽  
Nonlinear Semidefinite Programming ◽  
Kkt System ◽  
Problem Data

It was proved in Izmailov and Solodov (2014). Newton-Type Methods for Optimization and Variational Problems, Springer] that the existence of a noncritical multiplier for a (smooth) nonlinear programming problem is equivalent to an error bound condition for the Karush–Kuhn–Thcker (KKT) system without any assumptions. This paper investigates whether this result still holds true for a (smooth) nonlinear semidefinite programming (SDP) problem. The answer is negative: the existence of noncritical multiplier does not imply the error bound condition for the KKT system without additional conditions, which is illustrated by an example. In this paper, we obtain characterizations, in terms of the problem data, the critical and noncritical multipliers for a SDP problem. We prove that, for the SDP problem, the noncriticality property can be derived from the error bound condition for the KKT system without any assumptions, and we give an example to show that the noncriticality does not imply the error bound for the KKT system. We propose a set of assumptions under which the error bound condition for the KKT system can be derived from the noncriticality property. a Finally, we establish a new error bound for [Formula: see text]-part, which is expressed by both perturbation and the multiplier estimation.

scholarly journals EXPLOITING SPARSITY IN THE MATRIX-DILATION APPROACH TO ROBUST SEMIDEFINITE PROGRAMMING

2009 ◽  
Vol 52 (3) ◽  
pp. 321-338 ◽  
Author(s):  
Yasuaki Oishi ◽  
Yusuke Isaka
Keyword(s):  
Semidefinite Programming ◽  
The Matrix ◽  
Matrix Dilation

Homogeneous Self-Dual Algorithms for Stochastic Semidefinite Programming

2011 ◽  
Author(s):  
Shengping Jin ◽  
K. A. Ariyawansa ◽  
Yuntao Zhu
Keyword(s):  
Semidefinite Programming ◽  
Stochastic Semidefinite Programming

scholarly journals Towards a computational proof of Vizing's conjecture using semidefinite programming and sums-of-squares

2021 ◽  
Vol 107 ◽  
pp. 67-105
Author(s):  
Elisabeth Gaar ◽  
Daniel Krenn ◽  
Susan Margulies ◽  
Angelika Wiegele
Keyword(s):  
Semidefinite Programming ◽  
Sums Of Squares
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