A geometric characterization of strong duality in nonconvex quadratic programming with linear and nonconvex quadratic constraints

2013 ◽  
Vol 145 (1-2) ◽  
pp. 263-290 ◽  
Author(s):  
Fabián Flores-Bazán ◽  
Gabriel Cárcamo
Keyword(s):  
Quadratic Programming ◽  
Strong Duality ◽  
Geometric Characterization ◽  
Nonconvex Quadratic Programming ◽  
Quadratic Constraints

scholarly journals A Global Optimization Algorithm for Generalized Quadratic Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hongwei Jiao ◽  
Yongqiang Chen
Keyword(s):  
Linear Programming ◽  
Global Optimization ◽  
Quadratic Programming ◽  
Optimization Algorithm ◽  
Global Minimum ◽  
Nonconvex Programming ◽  
Nonconvex Quadratic Programming ◽  
Global Optimization Algorithm ◽  
Quadratic Constraints ◽  
Linear Programming Problems

We present a global optimization algorithm for solving generalized quadratic programming (GQP), that is, nonconvex quadratic programming with nonconvex quadratic constraints. By utilizing a new linearizing technique, the initial nonconvex programming problem (GQP) is reduced to a sequence of relaxation linear programming problems. To improve the computational efficiency of the algorithm, a range reduction technique is employed in the branch and bound procedure. The proposed algorithm is convergent to the global minimum of the (GQP) by means of the subsequent solutions of a series of relaxation linear programming problems. Finally, numerical results show the robustness and effectiveness of the proposed algorithm.

scholarly journals A characterization of the weighted version of McEliece–Rodemich–Rumsey–Schrijver number based on convex quadratic programming

2015 ◽  
Vol 07 (04) ◽  
pp. 1550050
Author(s):  
Carlos J. Luz
Keyword(s):  
Quadratic Programming ◽  
Discrete Math ◽  
Convex Quadratic Programming ◽  
Stability Number ◽  
Weighted Version ◽  
Similar Characterization ◽  
Number Formula ◽  
Weighted Stability ◽  
Theta Number

For any graph [Formula: see text] Luz and Schrijver [A convex quadratic characterization of the Lovász theta number, SIAM J. Discrete Math. 19(2) (2005) 382–387] introduced a characterization of the Lovász number [Formula: see text] based on convex quadratic programming. A similar characterization is now established for the weighted version of the number [Formula: see text] independently introduced by McEliece, Rodemich, and Rumsey [The Lovász bound and some generalizations, J. Combin. Inform. Syst. Sci. 3 (1978) 134–152] and Schrijver [A Comparison of the Delsarte and Lovász bounds, IEEE Trans. Inform. Theory 25(4) (1979) 425–429]. Also, a class of graphs for which the weighted version of [Formula: see text] coincides with the weighted stability number is characterized.

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