Fukushima, Masao Merit functions for variational inequality and complementarity problems. (English) Zbl 0996.90082 Di Pillo, Gianni (ed.) et al., Nonlinear optimization and applications. Proceedings of the 21st workshop, Erice, Italy, June 13-21, 1995. New York, NY: Plenum Press. 155-170 (1996). Summary: This paper presents an overview of the recent effort in reformulating the variational inequality problem and the complementarity problem as an equivalent optimization problem with certain desirable properties. Merit functions used to formulate such equivalent optimization problems turn out to be useful in designing a globally convergent algorithm and provide error bounds for those problems under appropriate conditions. See Zbl 0936.90052 for an update of this survey.For the entire collection see [Zbl 0941.00047]. Cited in 57 Documents MSC: 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 49J40 Variational inequalities Keywords:gap function; meri functions; overview; variational inequality problem; complementarity problem Citations:Zbl 0936.90052 PDFBibTeX XMLCite \textit{M. Fukushima}, in: Nonlinear optimization and applications. Proceedings of the 21st workshop, Erice, Italy, June 13--21, 1995. New York, NY: Plenum Press. 155--170 (1996; Zbl 0996.90082)