6 citations · 11 across the 8 of their papers we have counts for
9 papers · 1 filter
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…
Lagrange Multipliers, Duality, and Sensitivity in Set-Valued Convex Programming via Pointed Closed Convex Processes
Fernando García-Castaño, M. A. Melguizo Padial
We present a new kind of Lagrangian duality theory for set-valued convex optimization problems whose objective and constraint maps are defined between preordered normed spaces. The…
Sublinear Scalarizations for Proper and Approximate Proper Efficient Points in Nonconvex Vector Optimization
Fernando García-Castaño, Miguel Ángel Melguizo-Padial, G. Parzanese
We show that under a separation property, a -minimal point in a normed space is the minimum of a given sublinear function. This fact provides sufficient conditions, vi…
Existence and Density Theorems of Henig Global Proper Efficient Points
Fernando García-Castaño, Miguel Ángel Melguizo-Padial
In this work, we provide some novel results that establish both the existence of Henig global proper efficient points and their density in the efficient set for vector optimization…