6 citations · 19 across the 11 of their papers we have counts for
12 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…
A Set-Valued Lagrange Theorem based on a Process for Convex Vector Programming
Fernando García-Castaño, M. A. Melguizo Padial
In this paper, we present a new set-valued Lagrange multiplier theorem for constrained convex set-valued optimization problems. We introduce the novel concept of Lagrange process.…
On dentability and cones with a large dual
Fernando García-Castaño, M. A. Melguizo Padial
In this paper, we provide some equivalences on dentability in normed spaces. Among others we prove: the origin is a denting point of a pointed cone if and only if it is a point…
Denting Points of Convex Sets and Weak Property () of Cones in Locally Convex Spaces
Fernando García-Castaño, M. A. Melguizo Padial, G. Parzanese
In this paper we first extend from normed spaces to locally convex spaces some characterizations of denting points in convex sets. On the other hand, we also prove that in an infra…
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…