Duality without constraint qualification in nonsmooth optimization.
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-distance convergence of parametrised sums of convex functions in non-reflexive spaces.
Erratum for higher-order weakly generalized adjacent epiderivatives and applications to duality of set-valued optimization.
Error bounds for convex constrained systems in Banach spaces
Error estimate for optimality of distributed parameter control problems via duality.
Flow problems and duality.
Generalized convexity and optimization problems
Generalized quasi-variational inequalities and duality.
Generalized second-order mixed symmetric duality in nondifferentiable mathematical programming.
Harmonic sum and duality.
Higher-order weakly generalized adjacent epiderivatives and applications to duality of set-valued optimization.
Integral characterization of functionals defined on spaces of functions
Lagrangean decomposition for integer programming : theory and applications
Lagrangian stability and global optimality in nonconvex quadratic minimization over Euclidean balls and spheres.
Linear fractional functional programming in complex space
Minimax control of nonlinear evolution equations
In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.
Mixed-type duality for multiobjective fractional variational control problems.
Multifonctions s.c.i. et régularisée s.c.i. essentielle
Nonconvex Duality and Semicontinuous Proximal Solutions of HJB Equation in Optimal Control
In this work, we study an optimal control problem dealing with differential inclusion. Without requiring Lipschitz condition of the set valued map, it is very hard to look for a solution of the control problem. Our aim is to find estimations of the minimal value, (α), of the cost function of the control problem. For this, we construct an intermediary dual problem leading to a weak duality result, and then, thanks to additional assumptions of monotonicity of proximal subdifferential, we give a more...