6 citations · 11 across the 8 of their papers we have counts for
9 papers
Directionally Fine Families of Cones: Construction Principles, Approximation, and Separation
Fernando García-Castaño, Miguel Ángel Melguizo-Padial
We introduce the notion of a directionally fine family of cones, a local geometric property expressing the possibility of selecting arbitrarily narrow cones around every direction…
Norm-Cone Conjugation for Nonconvex Optimization: Scalar Duality and Exact Distance Penalization
Fernando García-Castaño, Miguel Ángel Melguizo-Padial
We develop a norm-cone conjugation framework, generated by translated norm-cones \[ x\mapsto r-α\|x-x_0\|, \qquad α\geq 0. \] We show that this family generates the same abstract-c…
Separation of Regular Co-Radiant Sets via Inner Approximating Sequences, Radial Profile Functions and Applications to Optimization
Fernando García-Castaño, Miguel Angel Melguizo-Padial
We develop a new framework for the analysis of co-radiant sets based on a new notion of regularity. This framework extends the classical theory beyond co-radiant sets admitting a n…
Process-Based Lagrange Multipliers for Nonconvex Set-Valued Optimization
Fernando García-Castaño, Miguel Ángel Melguizo-Padial
We develop a Lagrange multiplier theory for nonconvex set-valued optimization problems under Lipschitz-type regularity conditions. Instead of classical continuous linear functional…
Nonlinear Separation Theorems for Co-Radiant Sets and Optimality Conditions for Approximate and Proper Approximate Solutions in Vector Optimization
Fernando García-Castaño, Miguel Ángel Melguizo-Padial
This paper deals with -efficient and -properly efficient points with respect to a co-radiant set in vector optimization problems. In the first part of the…
Symmetric and Non-Symmetric Cone Separation via Bishop-Phelps Cones in Normed Spaces
Fernando García-Castaño, Christian Günther, M. A. Melguizo-Padial +1
In this paper, we study relationships between symmetric and non-symmetric separation of (not necessarily convex) cones by using separating cones of Bishop-Phelps type in real norme…