拟凸函数极小化问题解的存在性

Existence of Solutions for Quasiconvex Function Minimization Problems

考虑自反Banach空间中拟凸函数极小值问题解集的非空有界性.首先,给出非空闭凸集上拟凸函数的q-渐近函数定义及拟凸函数极小值问题解集存在性的等价刻画;其次,将经典凸函数极小值问题解集的非空有界性结果推广到拟凸函数上,并给出平衡问题解集非空有界的一个充分条件.

We considered nonempty boundness of solution sets for the quasiconvex function minimization problems in reflexive Banach spaces,gave the definition of q-asymptotic function of quasiconvex function on the nonempty closed convex set,and obtained the equivalent characterization of the existence of the solution set of the quasiconvex function minimization problems.The nonempty boundness of the solution set of the classical minimization problem of convex function was extended to quasiconvex function,and a sufficient condition for the nonempty boundness of the solution set of equilibrium problems was given.