UAB Digital Repository of Documents 12 records found  1 - 10next  jump to record: Search took 0.01 seconds. 
1.
21 p, 1.1 MB A general nonconvex multiduality principle / Bonenti, Francesca (Open Capital Partners SGR) ; Martínez-Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d’Economia i d’Història Econòmica) ; Riccardi, Rossana (Università degli Studi di Brescia. Dipartimento di Economia e Management)
We introduce a (possibly infinite) collection of mutually dual nonconvex optimization problems, which share a common optimal value, and give a characterization of their global optimal solutions. As immediate consequences of our general multiduality principle, we obtain Toland–Singer duality theorem as well as an analogous result involving generalized perspective functions. [...]
2018 - 10.1007/s10957-018-1245-1#citeas
Journal of Optimization Theory and Applications, Vol. 176, Núm. 3 (2018) , p. 527-540  
2.
9 p, 291.8 KB A generalization of the strong Fitzpatrick inequality / Elias, Leonardo M. (Universidade Federal do Paraná) ; Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)
We present a generalization of the strong Fitzpatrick inequality in the context of reflexive Banach spaces, involving a twisted bigger conjugate function. We also introduce a related family of gap functions for maximal monotone inclusion problems.
2017 - 10.1080/02331934.2016.1179738
Optimization, Vol. 6, Num. 6 (2017) , p.917-923  
3.
9 p, 328.3 KB Differentiability v.s. convexity for complementarity functions / Huang, Chien-Hao (National Taiwan Normal University. Department of Mathematics) ; Chen, Jein-Shan (National Taiwan Normal University. Department of Mathematics) ; Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d’Economia i d’Història Econòmica)
It is known that complementarity functions play an important role in dealing with complementarity problems. The most well known complementarity problem is the symmetric cone complementarity problem (SCCP) which includes nonlinear complementarity problem (NCP), semidefinite complementarity problem (SDCP), and second-order cone complementarity problem (SOCCP) as special cases. [...]
2017 - 10.1007/s11590-015-0993-1
Optimization Letters, Vol. 11, Num. 1 (2017) , p. 209–216  
4.
15 p, 334.0 KB A simplified conjugation scheme for lower semi-continuous functions / Elias, Leonardo M. (Universidade Federal do Paraná. Programa de Pós-Graduação em Matemática) ; Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)
We present two generalized conjugation schemes for lower semi-continuous functions defined on a real Banach space whose norm is Fréchet differentiable off the origin, and sketch their applications to optimization duality theory. [...]
2016 - 10.1080/02331934.2015.1080700
Optimization, Vol. 65, Núm. 4 (2016)  
5.
8 p, 278.6 KB Optimality conditions for pseudoconvex minimization over convex sets defined by tangentially convex constraints / Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)
We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex sets defined by non necessarily convex functions, in terms of tangential subdifferentials. [...]
2015 - 10.1007/s11590-014-0822-y
Optimization Letters, Vol. 9, Núm. 5 (June 2015) , p. 1017-1023  
6.
14 p, 440.0 KB The contribution of K.-H. Elster to generalized conjugation theory and nonconvex duality / Martínez-Legaz, Juan-Enrique (Universitat Autònoma de Barcelona. Department d’Economia i d’Història Econòmica)
This article surveys the main contributions of K. -H. Elster to the theory of generalized conjugate functions and its applications to duality in nonconvex optimization.
2015 - 10.1080/02331934.2014.929683
Optimization, Vol. 64, Núm. 1 (2015) , p. 87-96  
7.
9 p, 292.0 KB On the existence of a saddle value / Bonenti, F. (Università degli Studi di Brescia. Dipartimento di Economia e Management) ; Martínez-Legaz, Juan-Enrique (Universitat Autònoma de Barcelona. Departament d’Economia i d’Història Econòmica)
In this work, we achieve a complete characterization of the existence of a saddle value, for bifunctions which are convex, proper, and lower semi continuous in their first argument, by considering new suitably defined notions of special directions of recession. [...]
2015 - 10.1007/s10957-014-0665-9
Journal of Optimization Theory and Applications, Vol. 165, Núm. 3 (2015) , P. 785-792  
8.
16 p, 444.8 KB γ-Active constraints in convex semi-infinite programming / Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica) ; Todorov, Maxim Ivanov (Universidad de las Américas) ; Zetina, Carlos Armando (Universidad de las Américas)
In this article, we extend the definition of γ-active constraints for linear semi-infinite programming to a definition applicable to convex semi-infinite programming, by two approaches. The first approach entails the use of the subdifferentials of the convex constraints at a point, while the second approach is based on the linearization of the convex inequality system by means of the convex conjugates of the defining functions. [...]
2014 - 10.1080/01630563.2014.895745
Numerical Functional Analysis and Optimization, Vol. 35, Núm. 7-9 (2014) , p. 1078-1094  
9.
5 p, 137.7 KB On Weierstrass extreme value theorem / Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)
2014 - 10.1007/s11590-012-0587-0
Optimization letters, Vol. 8, Núm. 1, (2014) , p. 391-394  
10.
15 p, 319.5 KB Motzkin predecomposable sets / Iusem, N. (Instituto de Matématica Pura e Aplicada) ; Martínez-Legaz, Juan-Enrique (Universitat Autònoma de Barcelona. Department d’Economia i d’Història Econòmica) ; Todorov, Maxim Ivanov (Universidad de las Américas. Departmento de Actuaría y Matemáticas)
We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i. [...]
2014 - 10.1007/s10898-013-0097-3
Journal of Global Optimization, Vol. 60, Núm. 4 (2014) , pp. 635–647  

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