Global ETD Search

1	Inverse strongly monotone operators and variational inequalities Chi, Wen-te 23 June 2009 (has links) In this paper, we report existing convergence results on monotone variational inequalities where the governing monotone operators are either strongly monotone or inverse strongly monotone. We reformulate the variational inequality problem as an equivalent fixed point problem and then use fixed point iteration method to solve the original variational inequality problem. In the case of strong monotonicity case we use the Banach¡¦s contraction principle to define out iteration sequence; while in the case of inverse strong monotonicity we use the technique of averaged mappings to define our iteration sequence. In both cases we prove strong convergence for our iteration methods. An application to a minimization problem is also included. convergence iteration projection minimization Lipschitzian operator Variational inequality inverse strongly monotone averaged mapping strongly monotone monotone fixed point
2	Projection Methods for Variational Inequalities Governed by Inverse Strongly Monotone Operators Lin, Yen-Ru 26 June 2010 (has links) Consider the variational inequality (VI) x* ∈C, ‹Fx, x - x ›≥0, x∈C () where C is a nonempty closed convex subset of a real Hilbert space H and F : C¡÷ H is a monotone operator form C into H. It is known that if F is strongly monotone and Lipschitzian, then VI () is equivalently turned into a fixed point problem of a contraction; hence Banach's contraction principle applies. However, in the case where F is inverse strongly monotone, VI () is equivalently transformed into a fixed point problem of a nonexpansive mapping. The purpose of this paper is to present some results which apply iterative methods for nonexpansive mappings to solve VI (). We introduce Mann's algorithm and Halpern's algorithm and prove that the sequences generated by these algorithms converge weakly and respectively, strongly to a solution of VI (*), under appropriate conditions imposed on the parameter sequences in the algorithms. fixed point Variational inequality Mann's algorithm projection monotone mapping demiclosedness principle Halpern's algorithm nonexpansive mapping inverse strongly monotone strongly monotone weak convergence strongly convergence
3	Convergece Analysis of the Gradient-Projection Method Chow, Chung-Huo 09 July 2012 (has links) We consider the constrained convex minimization problem: min_x∈C f(x) we will present gradient projection method which generates a sequence x^k according to the formula x^(k+1) = P_c(x^k − £\_k∇f(x^k)), k= 0, 1, ¡P ¡P ¡P , our ideal is rewritten the formula as a xed point algorithm: x^(k+1) = T_(£\k)x^k, k = 0, 1, ¡P ¡P ¡P is used to solve the minimization problem. In this paper, we present the gradient projection method(GPM) and different choices of the stepsize to discuss the convergence of gradient projection method which converge to a solution of the concerned problem. variable stepsize strongly monotone gradient gradient-projection method nonexpansive mappingsm optimality condition monotone operator
4	Iterative Methods for Minimization Problems over Fixed Point Sets Chen, Yen-Ling 02 June 2011 (has links) In this paper we study through iterative methods the minimization problem min_{x∈C} £K(x) (P) where the set C of constraints is the set of fixed points of a nonexpansive mapping T in a real Hilbert space H, and the objective function £K:H¡÷R is supposed to be continuously Gateaux dierentiable. The gradient projection method for solving problem (P) involves with the projection P_{C}. When C = Fix(T), we provide a so-called hybrid iterative method for solving (P) and the method involves with the mapping T only. Two special cases are included: (1) £K(x)=(1/2)\|\|x-u\|\|^2 and (2) £K(x)=<Ax,x> - <x,b>. The first case corresponds to finding a fixed point of T which is closest to u from the fixed point set Fix(T). Both cases have received a lot of investigations recently. Halpern's algorithm demiclosedness principle hybrid method quadratic optimization strongly monotone monotone mapping projection iterative method fixed point nonexpansive mapping Minimization
5	Iterative Approaches to the Split Feasibility Problem Chien, Yin-ting 23 June 2009 (has links) In this paper we discuss iterative algorithms for solving the split feasibility problem (SFP). We study the CQ algorithm from two approaches: one is an optimization approach and the other is a fixed point approach. We prove its convergence first as the gradient-projection algorithm and secondly as a fixed point algorithm. We also study a relaxed CQ algorithm in the case where the sets C and Q are level sets of convex functions. In such case we present a convergence theorem and provide a different and much simpler proof compared with that of Yang [7]. firmly nonexpansive mapping relaxed CQ algorithm. CQ algorithm gradient projectionalgorithm projection averaged mapping Split feasibility problem inverse strongly monotone operator
6	Complementarity Problems Lin, Yung-shen 30 July 2007 (has links) In this thesis, we report recent results on existence for complementarity problems in infinite-dimensional spaces under generalized monotonicity are reported. generalized complementarity problem strongly pseudomonotone operators hemicontinuous operators strictly pseudomonotone operators pseudomonotone operators variational inequality strictly monotone operators strongly monotone operators complementarity problem monotone operators

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