Some relations between variational-like inequalities and efficient solutions of certain nonsmooth optimization problems.
Some remarks on the space of differences of sublinear functions
Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel conjugate of...
Some Representation Theorems for Functions and Sets and their Application to Nonlinear Programming.
Spatially-distributed coverage optimization and control with limited-range interactions
This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect...
Spatially-distributed coverage optimization and control with limited-range interactions
This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with...
Strict convex regularizations, proximal points and augmented lagrangians
Strict convex regularizations, proximal points and augmented lagrangians
Proximal Point Methods (PPM) can be traced to the pioneer works of Moreau [16], Martinet [14, 15] and Rockafellar [19, 20] who used as regularization function the square of the Euclidean norm. In this work, we study PPM in the context of optimization and we derive a class of such methods which contains Rockafellar's result. We also present a less stringent criterion to the acceptance of an approximate solution to the subproblems that arise in the inner loops of PPM. Moreover, we introduce a new...
Strongly quasiconvex quadratic functions.
Strong-weak Stackelberg Problems in Finite Dimensional Spaces
We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation...
Sufficient Second Order Optimality Conditions for C^1 Multiobjective Optimization Problems
2000 Mathematics Subject Classification: Primary 90C29; Secondary 90C30.In this work, we use the notion of Approximate Hessian introduced by Jeyakumar and Luc [19], and a special scalarization to establish sufficient optimality conditions for constrained multiobjective optimization problems. Throughout this paper, the data are assumed to be of class C^1, but not necessarily of class C^(1.1).
Sum-Of-Squares Clustering on Networks
Superlinear Convergence of Symmetric Huang's Class of Methods.
Sur des méthodes d'optimisation par relaxation
Sur la convergence de la méthode d'Adomian
Sur la convergence théorique de la méthode du gradient réduit généralisé.
Sur la dérivation numérique en optimisation
Sur la méthode de sur-relaxation, dans le cas des problèmes avec contrainte : un résultat de convergence asymptotique
Sur quelques méthodes de gradient réduit sous contraintes linéaires
Symbolic Implementation of the Hooke-Jeeves Method
Symmetric and self duality for a class of non-linear programming problems in complex space