Abstract
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.
Highlights
We focus on the following nonconvex minimization model problem: min f (x)
In [5, 11], some global optimality conditions for nonconvex minimization problems were derived by employing quadratic overestimators or underestimators of the object function that allows for the applications of the S-lemma
We present some global optimality conditions including necessary conditions and sufficient conditions for nonlinear programming problems over a quadratic inequality constraint extending several known global optimality conditions in the existing literature
Summary
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. Some global optimality conditions for nonconvex quadratic minimization problems with quadratic and/or linear constraints were recently developed in [6,7,8,9,10,11]. In [5, 11], some global optimality conditions for nonconvex minimization problems were derived by employing quadratic overestimators or underestimators of the object function that allows for the applications of the S-lemma.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
