scholarly journals Global optimality conditions for nonconvex minimization problems with quadratic constraints

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Guoquan Li ◽  
Zhiyou Wu ◽  
Jing Quan
Keyword(s):  
Optimality Conditions ◽  
Global Optimality ◽  
Global Optimality Conditions ◽  
Quadratic Constraints ◽  
Nonconvex Minimization ◽  
Minimization Problems

scholarly journals Global Optimality Conditions for Nonlinear Programming Problems with Linear Equality Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Guoquan Li ◽  
Yan Wang
Keyword(s):  
Optimality Conditions ◽  
Inequality Constraint ◽  
Local Minimizer ◽  
Global Minimizer ◽  
Global Optimality ◽  
Global Optimality Conditions ◽  
Nonconvex Minimization ◽  
Quadratic Inequality ◽  
Linear Equality ◽  
Necessary Global Optimality Conditions

Some necessary global optimality conditions and sufficient global optimality conditions for nonconvex minimization problems with a quadratic inequality constraint and a linear equality constraint are derived. In particular, global optimality conditions for nonconvex minimization over a quadratic inequality constraint which extend some known global optimality conditions in the existing literature are presented. Some numerical examples are also given to illustrate that a global minimizer satisfies the necessary global optimality conditions but a local minimizer which is not global may fail to satisfy them.

scholarly journals Unified global optimality conditions for smooth minimization problems with mixed variables

2008 ◽  
Vol 42 (3) ◽  
pp. 361-370 ◽  
Author(s):  
Vaithilingam Jeyakumar ◽  
Sivakolundu Srisatkunarajah ◽  
Nguyen Quang Huy
Keyword(s):  
Optimality Conditions ◽  
Global Optimality ◽  
Global Optimality Conditions ◽  
Mixed Variables ◽  
Minimization Problems
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