3 citations · 5 across the 12 of their papers we have counts for
13 papers
Robust generalized S-Procedure
N. Dinh, M. A. Goberna, D. H. Long +1
We introduce in this paper the so-called robust generalized S-procedure associated with a given robust optimization problem. We provide a primal characterization for the validity o…
Primal and Dual Characterizations for Farkas type Lemmas in Terms of Closedness Criteria
Nguyen Dinh, Miguel A. Goberna, Michel Volle
This paper deals with the characterization, in terms of closedness of certain sets regarding other sets, of Farkas lemmas determining when the upperlevel set of a given convex func…
Around a Farkas type Lemma
Nguyen Dinh, Miguel A. Goberna, M. Volle
The first two authors of this paper asserted in Lemma 4 of "New Farkas-type constraint qualifications in convex infinite programming" (DOI: 10.1051/cocv:2007027) that a given rever…
Duality for convex infinite optimization on linear spaces
Miguel A. Goberna, Michel Volle
This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (…
Relaxed Lagrangian duality in convex infinite optimization: reverse strong duality and optimality
Nguyen Dinh, Miguel A. Goberna, Marco A. Lopez +1
We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a…
Relaxed Lagrangian duality in convex infinite optimization: reducibility and strong duality
Nguyen Dih, Miguel A. Goberna, Marco A. López +1
We associate with each convex optimization problem, posed on some locally convex space, with infinitely many constraints indexed by the set T, and a given non-empty family H of fin…
Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semidefinite Programs
Miguel A. Goberna, Vaithilingam Jeyakumar, Guoyin Li
The radius of robust feasibility provides a numerical value for the largest possible uncertainty set that guarantees robust feasibility of an uncertain linear conic program. This d…
Primal-dual optimization conditions for the robust sum of functions with applications
Nguyen Dinh, Miguel A. Goberna, Michel Volle
This paper associates a dual problem to the minimization of an arbitrary linear perturbation of the robust sum function introduced in DOI 10.1007/s11228-019-00515-2. It provides an…
Duality for the robust sum of functions
Nguyen Dinh, Miguel A. Goberna, Michel Volle
In this paper we associate with an infinite family of real extended functions defined on a locally convex space, a sum, called robust sum, which is always well-defined. We also ass…
Characterizations of robust and stable duality for linearly perturbed uncertain optimization problems
Nguyen Dinh, Miguel A. Goberna, Marco A. López +1
We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depe…
Optimality conditions in convex multiobjective SIP
Miguel A. Goberna, Nader Kanzi
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with…
Characterizing weak solutions for vector optimization problems
Nguyen Dinh, Miguel A. Goberna, Dang H. Long +1
This paper provides characterizations of the weak solutions of optimization problems where a given vector function from a decision space to an objective space , is "min…
Robust Solutions to Multi-Objective Linear Programs with Uncertain Data
M. A. Goberna, V. Jeyakumar, G. Li +1
In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula…