An Elementary Proof of the Existence of Solutions of a Monotone Variational Inequality in the Finite-Dimensional Case

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• 作者：Jean-Pierre Crouzeix
• 关键词：Variational inequalities ; Maximal monotone maps ; Existence of solutions ; 47H05 ; 49J40 ; 47J20
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：168
• 期：2
• 页码：441-445
• 全文大小：330 KB
• 参考文献：1.Hartman, P., Stampacchia, G.: On some linear elliptic differential equations. Acta Math. 115, 271–310 (1966)CrossRef MathSciNet MATH
  2.Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problem. Springer, Berlin (2003)
  3.Auslender, A., Teboulle, M.: Asymptotic Cones and Functions in Optimization and Variational Inequalities. Springer, Berlin (2003)MATH
  4.Crouzeix, J.-P., Ocaña, E.: Maximality is nothing but continuity. J. Convex Anal. 17, 521–534 (2010)MathSciNet MATH
  5.Crouzeix, J.-P.: Pseudomonotone variational inequality problems: existence of solutions. Math. Program. 78, 305–314 (1997)MathSciNet MATH
  
• 作者单位：Jean-Pierre Crouzeix (1)
  
  1. LIMOS, Campus Scientifique des Cézeaux, Université Blaise Pascal, 63170, Aubière, France
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

This short note shows that the existence of solutions of a finite-dimensional monotone variational inequality on a compact set can be proved with only very elementary tools. Keywords Variational inequalities Maximal monotone maps Existence of solutions