Foundations of Set-Semidefinite Optimization

2009 ◽  
pp. 259-284 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Johannes Jahn
Keyword(s):  
Semidefinite Optimization

scholarly journals Parametric analysis of semidefinite optimization

Optimization ◽  
2019 ◽  
Vol 69 (1) ◽  
pp. 187-216 ◽  
Author(s):  
Ali Mohammad-Nezhad ◽  
Tamás Terlaky
Keyword(s):  
Parametric Analysis ◽  
Semidefinite Optimization

scholarly journals A Mehrotra predictor-corrector interior-point algorithm for semidefinite optimization

2017 ◽  
Vol 41 ◽  
pp. 168-185
Author(s):  
Mohammad PIRHAJI ◽  
Maryam ZANGIABADI ◽  
Hossien MANSOURI
Keyword(s):  
Interior Point ◽  
Semidefinite Optimization ◽  
Interior Point Algorithm ◽  
Predictor Corrector

scholarly journals Lower bound for the cost of connecting tree with given vertex degree sequence

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Mikhail Goubko ◽  
Alexander Kuznetsov
Keyword(s):  
Lower Bound ◽  
Heuristic Algorithms ◽  
Degree Sequence ◽  
Real Life ◽  
Inequality Constraints ◽  
Topology Design ◽  
Semidefinite Optimization ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
The Cost

Abstract The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, etc. For the case of connecting trees with the given sequence of vertex degrees the cost of the optimal tree is shown to be bounded from below by the solution of a semidefinite optimization program with bilinear matrix inequality constraints, which is reduced to the solution of a series of convex programs with linear matrix inequality constraints. The proposed lower-bound estimate is used to construct several heuristic algorithms and to evaluate their quality on a variety of generated and real-life datasets.

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