Mathematical Programming: Series A and B
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Mathematical Programming: Series A and B
Homotopy method for a class of nonconvex Brouwer fixed-point problems
Applied Mathematics and Computation
Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem
Nonlinear Analysis: Theory, Methods & Applications
Homotopy method for solving variational inequalities
Journal of Optimization Theory and Applications
Exceptional families and existence theorems for variational inequality problems
Journal of Optimization Theory and Applications
Optimization Methods & Software
Solving generalized Nash equilibrium problem with equality and inequality constraints
Optimization Methods & Software
Solving the nonlinear complementarity problem via an aggregate homotopy method
International Journal of Computer Applications in Technology
A smoothing homotopy method for variational inequality problems on polyhedral convex sets
Journal of Global Optimization
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In this paper, for solving the finite-dimensional variational inequality problem$$(x-x*)^{T} F(x*)\geq 0, \quad \forall x\in X,$$where F is a$$C^r (r gt; 1)$$ mapping from X to Rn, X =$$ { x \in R^{n} : g(x) leq; 0}$$ is nonempty (not necessarily bounded) and$${\it g}({\it x}): R^{n} \rightarrow R^{m}$$ is a convex Cr+1 mapping, a homotopy method is presented. Under various conditions, existence and convergence of a smooth homotopy path from almost any interior initial point in X to a solution of the variational inequality problem is proven. It leads to an implementable and globally convergent algorithm and gives a new and constructive proof of existence of solution.