We first reformulate the KKT system derived from the problem into a system of semismooth equations by using the F-B NCP function. Under some conditions, a solution of the system of semismooth equations is a solution of the problem.
最优化思路第二步核心
Determination of a search direction dkd_kdk:
Basis of the methods: Taylor series of f(x) in a small vicinity surrounding point xkx_kxk:
f(xk+δ)=f(xk)+▽Tf(xk).δ+12δT.▽T.▽2f(xk).δ+O(∣∣δ∣∣3)\LARGE f(x_k+\delta)=f(x_k)+\bigtriangledown ^Tf(x
