Global optimization of concave functions subject to quadratic constraints: An application in nonlinear bilevel programming

1992 ◽  
Vol 34 (1) ◽  
pp. 125-147 ◽  
Author(s):  
Faiz A. Al-Khayyal ◽  
Reiner Horst ◽  
Panos M. Pardalos
Keyword(s):  
Global Optimization ◽  
Bilevel Programming ◽  
Concave Functions ◽  
Quadratic Constraints

Bilevel Programming: Global Optimization

2006 ◽  
pp. 163-167
Author(s):  
Viswanathan Visweswaran
Keyword(s):  
Global Optimization ◽  
Bilevel Programming

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.

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