硕士毕业论文模板下载(5)

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Abstract

The Complementarity Problems was studied by Cottle and Dantzig in 1963 for the first time,It is an important domain in applied mathematics. The Complementarity Problems have the contact relations between optimization theory and equalium theory,variational inequalities and represent a wide class of mathematical models related to economics,engineering,mechanics,elasticity,game theory etc.Vector complementary problems was first introduced and studied by Chen GY and Yang XQ in 1990.Since then,a large number of results for the vector variational inequality and vector

vector F-complementary problem,in

generalized

f

In this

study the existence of the solution and equivalence between

complementary problem and variational equality.This is divided into four chapters.

In chapter 1,We introduce the background of the complementarity problems and the branch of the mathematics corresponding complementary,aspect of the complementary and the type of the complementarity problems.

In chapter 2 ,We generalize f-complementarity problem which introduced by Huang and Fang to set-valuedf-complementarity problem,and using KKM theorem to prove the equivalence between set-valuedf-complementarity problem and corresponding variational equality problems.then,We generalize the concept which introduced by Huang and Li in [8] to vector case,and using monotone of set-value mapping,pseudomonotone,lemma 2.1.1 to prove the equivalence of this type of complementarity and corresponding variational equality problems.

In chapter 3,We first introduce basic concept about complementarity，then，we generalize the notion which introduced by Huang and Li to set-valued case, using bounded from above，pseudomonotone,srictly pseudomonotone,hemicontinuous,

KKM

theorem and minimax principle to prove the existence of the solution of

set-valued strong complementarity.

In chapter 4,we introduce z mapping, srictly pseudomonotone II,strong feasible set,weak feasible ing bounded from above to prove the existence of the least element of the feasible set.