Quadratically Constrained Problems

1999 ◽  
pp. 21-26
Author(s):  
Christodoulos A. Floudas ◽  
Pãnos M. Pardalos ◽  
Claire S. Adjiman ◽  
William R. Esposito ◽  
Zeynep H. Gümüş ◽  
...  
Keyword(s):  
Constrained Problems ◽  
Quadratically Constrained

scholarly journals Exact quadratic convex reformulations of mixed-integer quadratically constrained problems

2015 ◽  
Vol 158 (1-2) ◽  
pp. 235-266 ◽  
Author(s):  
Alain Billionnet ◽  
Sourour Elloumi ◽  
Amélie Lambert
Keyword(s):  
Mixed Integer ◽  
Constrained Problems ◽  
Quadratically Constrained

scholarly journals Interplay of non-convex quadratically constrained problems with adjustable robust optimization

2020 ◽  
Author(s):  
Immanuel Bomze ◽  
Markus Gabl
Keyword(s):  
Robust Optimization ◽  
Quadratic Forms ◽  
Optimization Problems ◽  
Numerical Range ◽  
Optimization Theory ◽  
Geometric Condition ◽  
Constrained Problems ◽  
Adjustable Robust Optimization ◽  
Quadratically Constrained ◽  
Copositive Matrix

Abstract In this paper we explore convex reformulation strategies for non-convex quadratically constrained optimization problems (QCQPs). First we investigate such reformulations using Pataki’s rank theorem iteratively. We show that the result can be used in conjunction with conic optimization duality in order to obtain a geometric condition for the S-procedure to be exact. Based upon known results on the S-procedure, this approach allows for some insight into the geometry of the joint numerical range of the quadratic forms. Then we investigate a reformulation strategy introduced in recent literature for bilinear optimization problems which is based on adjustable robust optimization theory. We show that, via a similar strategy, one can leverage exact reformulation results of QCQPs in order to derive lower bounds for more complicated quadratic optimization problems. Finally, we investigate the use of reformulation strategies in order to derive characterizations of set-copositive matrix cones. Empirical evidence based upon first numerical experiments shows encouraging results.

scholarly journals On multiparametric/explicit NMPC for Quadratically Constrained Problems

2018 ◽  
Vol 51 (20) ◽  
pp. 400-405 ◽  
Author(s):  
Nikolaos A. Diangelakis ◽  
Iosif S. Pappas ◽  
Efstratios N. Pistikopoulos
Keyword(s):  
Constrained Problems ◽  
Quadratically Constrained
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