Nonlinear Programming and Variational Inequality Problems: A Unified Approach

By Michael Patriksson. 1998

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Citations in the corpus

Frank-Wolfe Algorithms for Saddle Point Problems (2016, background): “Hammond (1984) showed that a FW algorithm with a step size of O (1 /t ) converges for the VIP (3) when the set Z is strongly convex, while FW with a generalized line-search on a saddle point problem is sometimes non-convergent when Z is a polytope (see also (Patriksson, 1999, § 3.1.1)).”
On iterative methods for equilibrium problems (2009, methodology): “methods, physical and mathematical formulation of problems 91) and (2); see [1-20].”
Auxiliary Principle Technique for Equilibrium Problems (2004, unknown): “(9) Now, using ( 9 ), we have 0 ≤ F( vt ,v t ) ≤ tF(v t ,v )+ (1 − t)F(v t ,u ) ≤ tF(v t ,v )+ t( 1 − t){ϕ(v, u)− ϕ(u, u)}.”
Proximal Newton-Type Methods for Minimizing Composite Functions (2012, methodology): “We refer to Patriksson [20] for a unified treatment of descent methods for solving a large class of generalized equations.”
Existence of solutions for variational inequalities on Riemannian manifolds (2009, background): “Variational inequality problems on finite-dimensional Banach spaces are powerful tools for studying constrained optimization problems and equilibrium problems as well as complementary problems, and have been studied extensively, see for example the survey [1,2].”
Application of the Proximal Point Method to Nonmonotone Equilibrium Problems (2003, methodology): “Suppose that a sequence {x k } is generated by the method (4)–( 5 ) and that Ωk ≠∅ for”
Invex equilibrium problems (2005, methodology): “For the recent applications, numericals methods and formulations of variational inequalities, variational-like inequalities and equilibrium problems, see [1–41] and the references therein.”
Combined Relaxation Method for Mixed Equilibrium Problems (2005, methodology): “Thus, the bifunction h in ( 3 ) can be interpreted as the nonsmooth part of the bifunction � . In the following, we intend to present a method for (MEP) which generates a convergent sequence, even for nonmonotone G and h. More precisely, let us consider the problem of finding an element x ∗ ∈ X such”
New Trends in General Variational Inequalities (2020, methodology): “For recent state-of-the-art in this field, see [1-200] and the references therein.”
Mixed variational inequalities and economic equilibrium problems (2002, unknown): “1) and suggest various solution methods, including descent methods with respect to a so-called merit function; for example, see [22].”