Research On LC～1 Optimization Algorithms

This paper is organized as follows: In the first chapter, we briefly review the origin and development of the nonlinear optimization problems and LC1 optimization problems, and the optimization conditions were presented . LC1 unconstrained optimization problem was discussed in the second chapter, giving a new trust region method and proving its global convergence and superlinear convergence under some mild conditions . In the third chapter we discuss LC1 constrained optimization problem . To solve it, we turn it into nonsmooth equations, utilizing inexact theory we give an inexact generalized Newton's method and under some mild conditions we prove that it is global convergence and superlinear convergence .