Radiality and semismoothness
Random perturbation of the variable metric method for unconstrained nonsmooth nonconvex optimization
We consider the global optimization of a nonsmooth (nondifferentiable) nonconvex real function. We introduce a variable metric descent method adapted to nonsmooth situations, which is modified by the incorporation of suitable random perturbations. Convergence to a global minimum is established and a simple method for the generation of suitable perturbations is introduced. An algorithm is proposed and numerical results are presented, showing that the method is computationally effective and stable....
Regular maximal monotone operators and the sum theorem.
Relación entre conos de direcciones decrecientes y conos de direcciones de descenso.
Sea f: N → R una función convexa y sea x ∈ Ni, donde N es un convexo en un espacio vectorial real. Se demuestra que, si Df<(x) es no vacío, entonces Df<(x) es el interior algebraico de Df≤(x).
Relationship between dynamic programming and the maximum principle under state constraints.
Remarks on second order generalized derivatives for differentiable functions with Lipschitzian Jacobian.
Restrictive metric regularity and generalized differential calculus in Banach spaces.
Rotundity, smoothness and duality