Descent methods for convex optimization problems in Banach spaces.
Deux algorithmes de programmation mathématique
Duality and optimality conditions in abstract concave maximization
Duality for optimal control-approximation problems with gauges.
Duality in Constrained DC-Optimization via Toland’s Duality Approach
2000 Mathematics Subject Classification: 90C48, 49N15, 90C25In this paper we reconsider a nonconvex duality theory established by B. Lemaire and M. Volle (see [4]), related to a primal problem of minimizing the difference of two convex functions subject to a DC-constraint. The purpose of this note is to present a new method based on Toland-Singer duality principle. Applications to the case when the constraints are vector-valued are provided.
Duality in vector optimization. II. Vector quasiconcave programming
Duality of transformation functions in the interior point methods.
Dykstra's algorithm as the nonlinear extension of Bregman's optimization method.
Employing different loss functions for the classification of images via supervised learning
Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions....
Epi/hypo-convergence: The slice topology and saddle points approximation.
Équivalences concernant la séparation de plusieurs cônes convexes
Estimating Matrices.
Estimation of the derivative of the convex function by means of its uniform approximation.
Event-triggered design for multi-agent optimal consensus of Euler-Lagrangian systems
In this paper, a distributed optimal consensus problem is investigated to achieve the optimization of the sum of local cost function for a group of agents in the Euler-Lagrangian (EL) system form. We consider that the local cost function of each agent is only known by itself and cannot be shared with others, which brings challenges in this distributed optimization problem. A novel gradient-based distributed continuous-time algorithm with the parameters of EL system is proposed, which takes the distributed...
Extension de la méthode Procuste à la comparaison de nuages de points situés dans des espaces de dimensions différentes
Extensions of convex functionals on convex cones
We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.
Extensions of cyclically monotone mappings
Extreme points of a convex polytope and extreme rays of the corresponding convex cone
Extremum conditions for nonlinear functions on convex sets
Fejer Methods for Solving Infinite Systems of Convex Inequalities