Abstract
In this survey chapter, we present systems of various kinds of vector quasi-equilibrium problems and give existence theory for their solutions. Some applications to systems of vector quasi-optimization problems, quasi-saddle point problems for vector-valued functions and Debreu type equilibrium problems, also known as constrained Nash equilibrium problems, for vector-valued functions are presented. The investigations of this chapter are based on our papers: Ansari (J Math Anal Appl 341:1271–1283, 2008); Ansari et al. (J Global Optim 29:45–57, 2004); Ansari and Khan (Mathematical Analysis and Applications, edited by S. Nanda and G.P. Rajasekhar, Narosa, New Delhi, 2004, pp.1–13); and Ansari et al. (J Optim Theory Appl 127:27–44, 2005).
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Keywords
- Equilibrium Problem
- Topological Vector Space
- Vector Variational Inequality
- Vector Equilibrium Problem
- Nash Equilibrium Problem
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Ansari, Q.H., Yao, JC. (2010). Systems of Vector Quasi-equilibrium Problems and Their Applications. In: Burachik, R., Yao, JC. (eds) Variational Analysis and Generalized Differentiation in Optimization and Control. Springer Optimization and Its Applications, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0437-9_1
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