A Generalized Convexity and Variational Inequality for Quasi-Convex Minimization
Phan Thiên Thach, Masakazu Kojima · SIAM Journal on Optimization · 1996
We present a variational-type necessary and sufficient condition for the optimality in a quasi-convex minimization, in which a vanishing differential is not a sufficient condition. Using this condition we show that path-following methods can, in principle, be applied to solving a quasi-convex minimization. Also, we givee a connection between an optimality condition and a duality scheme using a minimax principle.