Existence theorems for the implicit complementarity problem.
Extrema with constraints on points and/or velocities.
Fritz John's type conditions and associated duality forms in convex non differentiable vector-optimization
Generalized Newton and NCP-methods: convergence, regularity, actions
Solutions of several problems can be modelled as solutions of nonsmooth equations. Then, Newton-type methods for solving such equations induce particular iteration steps (actions) and regularity requirements in the original problems. We study these actions and requirements for nonlinear complementarity problems (NCP's) and Karush-Kuhn-Tucker systems (KKT) of optimization models. We demonstrate their dependence on the applied Newton techniques and the corresponding reformulations. In this way, connections...
Generic well-posedness for a class of equilibrium problems.
Generic well-posedness in some classes of optimization problems
Geodesic algorithms in Riemannian geometry.
Iterative approximation to convex feasibility problems in Banach space.
Iterative methods for nonlinear quasi complementarity problems.
Kantorovich spaces and optimization.
Lagrange multipliers method and quadratic programming in Hilbert space
Levitin-Polyak well-posedness for equilibrium problems with functional constraints.
Linear independences in bottleneck algebra and their coherences with matroids.
Méthodes du second ordre dans les problèmes d'optimisation avec contraintes
Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities
We propose a modification of the golden ratio algorithm for solving pseudomonotone equilibrium problems with a Lipschitz-type condition in Hilbert spaces. A new non-monotone stepsize rule is used in the method. Without such an additional condition, the theorem of weak convergence is proved. Furthermore, with strongly pseudomonotone condition, the $R$-linear convergence rate of the method is established. The results obtained are applied to a variational inequality problem, and the convergence rate...
Moreau's decomposition theorem revisited
New concepts in nondifferentiable programming
New Farkas-type constraint qualifications in convex infinite programming
This paper provides KKT and saddle point optimality conditions, duality theorems and stability theorems for consistent convex optimization problems posed in locally convex topological vector spaces. The feasible sets of these optimization problems are formed by those elements of a given closed convex set which satisfy a (possibly infinite) convex system. Moreover, all the involved functions are assumed to be convex, lower semicontinuous and proper (but not necessarily real-valued). The key result...
Nonlinear Duality And Multiplier Theorems.
Nonparametric Maximum Likelihood Estimation of a Probability Density via Mathematical Programming.