다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

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Convex Analysisの二,三の進展について

Introduction to stochastic programming

“Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.

SET-Valued Analysis

Well, someone can decide by themselves what they want to do and need to do but sometimes, that kind of person will need some theory of vector optimization references. People with open minded will always try to seek for the new things and information from many sources. On the contrary, people with closed mind will always think that they can do it by their principals. So, what kind of person are you?

Theory Of Vector Optimization

In this paper, the lower semicontinuity and continuity of the solution mapping to a parametric generalized vector equilibrium problem involving set-valued mappings are established by using a new proof method which is different from the ones used in the literature.

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Solution semicontinuity of parametric generalized vector equilibrium problems

In this paper, we present a projection method to solve monotone nonlinear equations with convex constraints. This method can be viewed as an extension of CG_DESCENT method which is one of the most effective conjugate gradient methods for solving unconstrained optimization problems. Because of derivative-free and low storage, the proposed method can be used to solve large-scale nonsmooth monotone nonlinear equations. Its global convergence is established under some appropriate conditions. Preliminary numerical results show that the proposed method is effective and promising. Moreover, we also successfully use the proposed method to solve the sparse signal reconstruction in compressive sensing.

A projection method for convex constrained monotone nonlinear equations with applications

This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector quasi-equilibrium problems are established.

Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems

This paper deals with higher-order optimality conditions of set-valued optimization problems. By virtue of the higher-order derivatives introduced in (Aubin and Frankowska, Set-Valued Analysis, Birkhauser, Boston, [1990]) higher-order necessary and sufficient optimality conditions are obtained for a set-valued optimization problem whose constraint condition is determined by a fixed set. Higher-order Fritz John type necessary and sufficient optimality conditions are also obtained for a set-valued optimization problem whose constraint condition is determined by a set-valued map.

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Shengjie Li

Papers

Solution semicontinuity of parametric generalized vector equilibrium problems

A projection method for convex constrained monotone nonlinear equations with applications

Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems

Higher-Order Optimality Conditions for Set-Valued Optimization

Higher order optimality conditions for Henig efficient solutions in set-valued optimization☆