PUBLICATIONS

 

 

 

Goberna, M.A.; Iusem, A.; Martínez-Legaz, J. E.; Todorov, M.I.
Motzkin decomposition of closed convex sets via truncation.
J. Math. Anal. Appl. 400 (2013), no. 1, 35–47.

Martínez-Legaz, J. E.; Vicente-Pérez, J.
Lexicographical representation of convex sets.
J. Convex Anal. 19 (2012), no. 2, 485–496.

García Ramos, Y.; Martínez-Legaz, J. E.; Simons, S.
New results on q-positivity.
Positivity 16 (2012), no. 3, 543–563.

Martínez-Legaz, J. E.; Martinón, A.
On the infimum of a quasiconvex vector function over an intersection.
TOP 20 (2012), no. 2, 503–516.

Mohebi, H.; Martínez-Legaz, J. E.; Rocco, M.
Some criteria for maximal abstract monotonicity.
J. Global Optim. 53 (2012), no. 2, 137–163.

Bilbao, J. M.; Martínez-Legaz, J. E.
A convex representation of totally balanced games.
J. Math. Anal. Appl. 387 (2012), no. 2, 1167–1175.

Martínez-Legaz, J. E.; Martinón, A.
On the infimum of a quasiconvex function over an intersection. Application to the distance function.
J. Convex Anal. 18 (2011), no. 3, 687–698.

Ginchev, I.; Martínez-Legaz, J. E.
Characterization of d.c. functions in terms of quasidifferentials.
Nonlinear Anal. 74 (2011), no. 17, 6781–6787.

Rocco, M.; Martínez-Legaz, J. E.
On surjectivity results for maximal monotone operators of type (D).
J. Convex Anal. 18 (2011), no. 2, 545–576
.

Martínez-Legaz, J. E.; Vicente-Pérez, J.
The e-support function of an e-convex set and conjugacy for e-convex functions.
J. Math. Anal. Appl. 376 (2011), no. 2, 602–612
.

Burachik, R. S.; Martínez-Legaz, J. E.; Rocco, M.
On a sufficient condition for equality of two maximal monotone operators.
Set-Valued Var. Anal. 18 (2010), no. 3-4, 327–335
.

Goberna, M. A.; Martínez-Legaz, J. E.; Todorov, M. I.
On Motzkin decomposable sets and functions.
J. Math. Anal. Appl. 372 (2010), no. 2, 525–537
.

Goberna, M. A.; González, E.; Martínez-Legaz, J. E.; Todorov, M. I.
Motzkin decomposition of closed convex sets.
J. Math. Anal. Appl. 364 (2010), no. 1, 209–221.

Martínez-Legaz, J. E.
Convexity of Indirect Utility Functions.
Homenaje al Dr. Antonio Martinón Cejas por su 60 cumpleaños, 153-159, San Cristóbal de La Laguna, 2010.

Martínez-Legaz, J. E.
On maximally qq-positive sets.
J. Convex Anal. 16 (2009), no. 3-4, 891–898.

Martínez-Legaz, J. E.
What is invexity with respect to the same ŋ?
Taiwanese J. Math. 13 (2009), no. 2B, 753-755.

Ferrer, A.; Martínez-Legaz, J. E.
Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function.
J. Global Optim. 43 (2009), no. 4, 513-531.

Martínez-Legaz, J. E.
Some generalizations of Rockafellar's surjectivity theorem.
Pac. J. Optim. 4 (2008), no. 3, 527–535.

Dutta, J.; Martínez-Legaz, J. E.; Rubinov, A. M.
Monotonic analysis over cones. III.
J. Convex Anal. 15 (2008), no. 3, 561-579.

Martínez-Legaz, J. E.; Singer, I.
Comparing Fenchel-Moreau conjugates with level set conjugates.
J. Convex Anal. 15 (2008), no. 2, 285-297.

Martínez-Legaz, J. E.; Svaiter, B. F.
Minimal convex functions bounded below by the duality product.
Proc. Amer. Math. Soc. 136 (2008), no. 3, 873-878.

Martínez-Legaz, J. E.; Soubeyran, A.
A Tabu Search Scheme for Abstract Problems, with Applications to the Computation of Fixed Points.
J. Math. Anal. Appl. 338 (2008), no. 1, 620-627.
Corrigendum: J. Math. Anal. Appl. 342 (2008), no. 2, 1493.

Martínez-Legaz, J. E.
Convex conjugation and duality for the solutions of a functional equation.
Vietnam J. Math. 35 (2007), no. 4, 481-493.

Martínez-Legaz, J. E.; Martinón, A.
Boundedly connected sets and the distance to the intersection of two sets.
J. Math. Anal. Appl. 332 (2007), no. 1, 400-406.

Hiriart-Urruty, J.-B.; Martínez-Legaz, J. E.
Convex solutions of a functional equation arising in information theory.
J. Math. Anal. Appl. 328 (2007), no. 2, 1309-1320.

Martínez-Legaz, J. E.; Quah, J. K.-H.
A contribution to duality theory, applied to the measurement of risk aversion.
Econom. Theory 30 (2007), no. 2, 337-362.

Martínez-Legaz, J. E.; Sosa, W.
Duality for equilibrium problems.
J. Global Optim. 35 (2006), no. 2, 311-319.

Martínez-Legaz, J. E.; Penot, J.-P.
Regularization by erasement.
Math. Scand. 98 (2006), no. 1, 97-124.

Martínez-Legaz, J. E.
Some characterizations of convex games.
Recent advances in optimization, 293-303, Lecture Notes in Econom. and Math. Systems, 563, Springer, Berlin, 2006.

Martínez-Legaz, J. E.; Singer, I.
Some conjugation formulas and subdifferential formulas of convex analysis revisited.
J. Math. Anal. Appl. 313 (2006), no. 2, 717-729..

Martínez-Legaz, J. E.
La interpretación económica de los multiplicadores de Lagrange
Matematicalia 2 (2006), no. 5, 1-8.

López, M. A.; Martínez-Legaz, J. E.
Farkas-type theorems for positively homogeneous semi-infinite systems.
Optimization 54 (2005), no. 4-5, 421-431.

Martínez-Legaz, J. E.; Rubinov, A. M.; Schaible, S.
Increasing quasiconcave co-radiant functions with applications in mathematical economics.
Math. Methods Oper. Res. 61 (2005), no. 2, 261-280.

Martínez-Legaz, J. E.
On Brickman's theorem.
J. Convex Anal. 12 (2005), no. 1, 139-143.

Martínez-Legaz, J. E.; Svaiter, B. F.
Monotone operators representable by l. s. c. convex functions.
Set-Valued Anal. 13 (2005), no. 1, 21-46.

Martínez-Legaz, J. E.
Generalized convex duality and its economic applications.
Handbook of generalized convexity and generalized monotonicity, 237-292, Nonconvex Optim. Appl., 76, Springer, New York, 2005.

Dutta, J.; Martínez-Legaz, J. E.; Rubinov, A. M.
Monotonic analysis over cones. II.
Optimization 53 (2004), no. 5-6, 529-547.

Dutta, J.; Martínez-Legaz, J. E.; Rubinov, A. M.
Monotonic analysis over cones. I.
Optimization 53 (2004), no. 2, 129-146.

Martínez-Legaz, J. E.
Banach's contractive mapping principle
An Eponymous Dictionary of Economics (A Guide to Laws and Theorems Named after Economists), 14-15, Edward Elgar, Cheltenham-Northampton, 2004
.

Martínez-Legaz, J. E.
Lagrange Multipliers
An Eponymous Dictionary of Economics (A Guide to Laws and Theorems Named after Economists), 143-144, Edward Elgar, Cheltenham-Northampton, 2004.

Hiriart-Urruty, J.-B.; Martínez-Legaz, J. E.
New formulas for the Legendre-Fenchel transform.
J. Math. Anal. Appl. 288 (2003), no. 2, 544-555.

Martínez-Legaz, J. E.; Meseguer, A.
The indirect function of an NTU game.
 J. Math. Sci. (N. Y.) 116 (2003), no. 3, 3253-3265.

Getán, J.; Martínez-Legaz, J. E.; Singer, I.
(*,s)-dualities.
J. Math. Sci. (N. Y.) 115 (2003), no. 4, 2506-2541.

Bilbao, J. M.; Martínez-Legaz, J. E.
Some applications of convex analysis to cooperative game theory.
J. Stat. Manag. Syst. 5 (2002), no. 1-3, 39-61.
MathSciNet

Daniilidis, A.; Martínez-Legaz, J. E.
Characterizations of evenly convex sets and evenly quasiconvex functions.
J. Math. Anal. Appl. 273 (2002), no. 1, 58-66.

Martínez-Legaz, J. E.; Rubinov, A. M.; Singer, I.
Downward sets and their separation and approximation properties.
J. Global Optim. 23 (2002), no. 2, 111-137.

Daniilidis, A.; Hadjisavvas, N.; Martínez-Legaz, J. E.
An appropriate subdifferential for quasiconvex functions.
SIAM J. Optim. 12 (2001/02), no. 2, 407-420

Martínez-Legaz, J. E.; Rubinov, A. M.
Increasing positively homogeneous functions defined on Rn.
Acta Math. Vietnam. 26 (2001), no. 3, 313-331.

Martínez-Legaz, J. E.; Volle, M.
Duality for d. c. optimization over compact sets.
Optimization theory (Mátraháza, 1999), 139-146, Appl. Optim., 59, Kluwer Acad. Publ., Dordrecht, 2001.
MathSciNet

Dragan, I.; Martínez-Legaz, J. E.
On the semivalues and the power core of cooperative TU games.
Int. Game Theory Rev. 3 (2001), no. 2-3, 127-139.

Martínez-Legaz, J. E.; Théra, M.
A convex representation of maximal monotone operators.
J. Nonlinear Convex Anal. 2 (2001), no. 2, 243-247.
MathSciNet

Martínez-Legaz, J. E.; Singer, I.
Semi-spaces and bases of convexity systems in complete lattices.
Constructive, experimental, and nonlinear analysis (Limoges, 1999), 235-243, CMS Conf. Proc., 27, Amer. Math. Soc., Providence, RI, 2000.
MathSciNet

Martínez-Legaz, J. E.
Optimización matemática y sus aplicaciones económicas

Varia Mathematica, 1, 97-153, Institut d’Estudis Ilerdencs, Lleida, 2000.

Bajona-Xandri, C.; Martínez-Legaz, J. E.
Lower subdifferentiability in minimax fractional programming.
Optimization 45 (1999), no. 1-4, 1-12.

Martínez-Legaz, J. E.
A new characterization of totally balanced games.
Topics in mathematical economics and game theory (Toronto, ON, 1995), 83-88, Fields Inst. Commun., 23, Amer. Math. Soc., Providence, RI, 1999.
MathSciNet

Luc, D. T.; Martínez-Legaz, J. E..; Seeger, A.
Least deviation decomposition with respect to a pair of convex sets.
J. Convex Anal. 6 (1999), no. 1, 115-140.

Martínez-Legaz, J. E.; Sach, P. H.
A new subdifferential in quasiconvex analysis.
J. Convex Anal. 6 (1999), no. 1, 1-11.

Martínez-Legaz, J. E.; Volle, M.
Duality in D.C. programming: the case of several D.C. constraints.
J. Math. Anal. Appl. 237 (1999), no. 2, 657-671.

Flores-Bazán, F.; Martínez-Legaz, J. E.
Simplified global optimality conditions in generalized conjugation theory.
Generalized convexity, generalized monotonicity: recent results (Luminy, 1996), 305-329, Nonconvex Optim. Appl., 27, Kluwer Acad. Publ., Dordrecht, 1998.
MathSciNet

Martínez-Legaz, J. E.; Singer, I.
On Φ-convexity of convex functions.
Linear Algebra Appl. 278 (1998), no. 1-3, 163-181.

Martínez-Legaz, J. E.
A duality theory for totally balanced games.
Proceedings of the IV Catalan Days of Applied Mathematics (Tarragona, 1998), 151-161, Univ. Rovira Virgili, Tarragona, 1998.
MathSciNet

Martínez-Legaz, J. E.
Lexicographic utility and orderings.
Handbook of Utility Theory, vol. 1. Kluwer Academic Publisher,, Dordrecht, The Netherlands, 1998.

Martinez-Legaz, J. E.; Singer, I.
On conjugations for functions with values in extensions of ordered groups.
Positivity 1 (1997), no. 3, 193-218.

Martínez-Legaz, J. E.
Characterization of R-evenly quasiconvex functions.
J. Optim. Theory Appl. 95 (1997), no. 3, 717-722.

Martínez-Legaz, J. E.; Singer, I.
An extension of d.c. duality theory, with an appendix on *-subdifferentials.
Optimization 42 (1997), no. 1, 9-37.

Martínez-Legaz, J. E.
Lexicographical characterization of the faces of convex sets.
Acta Math. Vietnam. 22 (1997), no. 1, 207-211.

Martínez-Legaz, J. E.; Théra, M.
ε-subdifferentials in terms of subdifferentials.
 Set-Valued Anal. 4 (1996), no. 4, 327-332.

Martínez-Legaz, J. E.
On the uniqueness of perfect matchings in bipartite graphs.
Exposition. Math. 14 (1996), no. 5, 473-480.
MathSciNet

Martínez-Legaz, J. E.
Dual representation of cooperative games based on Fenchel-Moreau conjugation.
Optimization 36 (1996), no. 4, 291-319.

Martínez-Legaz, J. E.; Santos, M. S.
On expenditure functions.
J. Math. Econom. 25 (1996), no. 2, 143-163.

Coutat, P.; Volle, M.; Martínez-Legaz, J. E.
Convex functions with continuous epigraph or continuous level sets.
J. Optim. Theory Appl. 88 (1996), no. 2, 365-379.

Martínez-Legaz, J. E.
On convex and quasiconvex spectral functions.
Proceedings of the 2nd Catalan Days on Applied Mathematics (Odeillo, 1995), 199-208, Collect. Études, Presses Univ. Perpignan, Perpignan, 1995.
MathSciNet

Martínez-Legaz, J. E.
Fenchel duality and related properties in generalized conjugation theory.
Southeast Asian Bull. Math. 19 (1995), no. 2, 99-106.
MathSciNet

Martínez-Legaz, J. E.; Singer, I.
Dualities associated to binary operations on $\overline R$.
J. Convex Anal. 2 (1995), no. 1-2, 185-209.

Martínez-Legaz, J. E.; Singer, I.
Subdifferentials with respect to dualities.
ZOR-Math. Methods Oper. Res. 42 (1995), no. 1, 109-125.

Crouzeix, J.-P.; Martínez-Legaz, J. E.; Seeger, A.
An alternative theorem for quadratic forms and extensions.
Linear Algebra Appl. 215 (1995), 121-134.

Martínez-Legaz, J. E.; Singer, I.
∗-dualities.
Optimization 30 (1994), no. 4, 295-315.

Martínez-Legaz, J. E.; Seeger, A.
A general cone decomposition theory based on efficiency.
Math. Programming 65 (1994), no. 1, Ser. A, 1-20.

Martínez-Legaz, J. E.; Seeger, A.
Yuan's alternative theorem and the maximization of the minimum eigenvalue function.
J. Optim. Theory Appl. 82 (1994), no. 1, 159-167.

Martínez-Legaz, J. E.; Singer, I.
Some characterizations of perturbational dual problems.
Optimization 29 (1994), no. 2, 97-130.

Boncompte, M.; Martínez-Legaz, J. E.
Weak lower subdifferentiability in fractional programming.
Int. Trans. Oper. Res. 1, No.2, 265-270 (1994).

Marchi, E.; Martínez-Legaz, J. E.
A generalization of Fan-Browder's fixed point theorem and its applications.
Topol. Methods Nonlinear Anal. 2 (1993), no. 2, 277-291.
MathSciNet

Martínez-Legaz, J. E.; Romano-Rodríguez, S.
α-lower subdifferentiable functions.
SIAM J. Optim. 3 (1993), no. 4, 800-825.

Martínez-Legaz, J. E.; Singer, I.
Some further characterizations of unperturbational dual problems.
Parametric optimization and related topics, III (Güstrow, 1991), 407-436, Approx. Optim., 3, Lang, Frankfurt am Main, 1993.
MathSciNet

Martínez-Legaz, J. E.
Axiomatic characterizations of the duality correspondence in consumer theory.
J. Math. Econom. 22 (1993), no. 6, 509-522.

Martínez-Legaz, J. E.; Romano-Rodríguez, S.
Lower subdifferentiability of quadratic functions.
Math. Programming 60 (1993), no. 1, Ser. A, 93-113.

Martínez-Legaz, J. E.; Santos, M. S.
Duality between direct and indirect preferences.
Econom. Theory 3 (1993), no. 2, 335-351.

Martínez-Legaz, J. E.; Singer, I.
Some characterizations of surrogate dual problems.
Optimization 24 (1992), no. 1-2, 1-11.

Crouzeix, J.-P.; Martínez-Legaz, J. E.; Seeger, A.
Un théorčme de l'alternative pour des formes quadratiques et quelques extensions.
C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), no. 7, 505-506.
MathSciNet

Martínez-Legaz, J. E.; Seeger, A.
A formula on the approximate subdifferential of the difference of convex functions.
Bull. Austral. Math. Soc. 45 (1992), no. 1, 37-41.

Martínez-Legaz, J. E.; Singer, I.
Some characterizations of φ-Lagrangian dual problems.
Optimization 22 (1991), no. 6, 835-843.

Marchi, E.; Martínez-Legaz, J. E.
Some results on approximate continuous selections, fixed points and minimax inequalities.
Fixed point theory and applications (Marseille, 1989), 327-343, Pitman Res. Notes Math. Ser., 252, Longman Sci. Tech., Harlow, 1991.
MathSciNet

Martínez-Legaz, J. E.; Singer, I.
Multi-order convexity.
Applied geometry and discrete mathematics, 471-488, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 4, Amer. Math. Soc., Providence, RI, 1991.
MathSciNet

Martínez-Legaz, J. E.
Characterizations of efficient solutions under polyhedrality assumptions.
Z. Oper. Res. 35 (1991), no. 3, 221-230.

Martínez-Legaz, J. E.; Singer, I.
Compatible preorders and linear operators on Rn.
Linear Algebra Appl. 153 (1991), 53-66.
Erratum: Linear Algebra Appl. 220 (1995), 5-6.

Martínez-Legaz, J. E.; Singer, I.
-dualities and -dualities.
Optimization  22 (1991), no. 4, 483-511.
Errata corrige: Optimization 24 (1992), no. 1-2, 13.

Boncompte, M.; Martínez-Legaz, J. E.
Fractional programming by lower subdifferentiability techniques.
J. Optim. Theory Appl. 68 (1991), no. 1, 95-116.

Martínez-Legaz, J. E.
Duality between direct and indirect utility functions under minimal hypotheses.
J. Math. Econom. 20 (1991), no. 2, 199-209.

Martínez-Legaz, J. E.
Uniform approximation by classes of functions closed under translation and pointwise supremum.
Numer. Funct. Anal. Optim. 11 (1991), no. 9-10, 967-986.

Martínez-Legaz, J. E.; Singer, I.
A characterization of Lagrangian dual problems.
Note Mat. 10 (1990), suppl. 2, 389-394.

Martínez-Legaz, J. E.
Generalized conjugation and related topics.
Generalized convexity and fractional programming with economic applications (Pisa, 1988), 168-197, Lecture Notes in Econom. and Math. Systems, 345, Springer, Berlin, 1990.
MathSciNet

Martínez-Legaz, J. E.; Singer, I.
Dualities between complete lattices.
Optimization 21 (1990), no. 4, 481-508.

Martínez-Legaz, J. E.
Weak lower subdifferentials and applications.
Optimization 21 (1990), no. 3, 321-341.

Martínez-Legaz, J. E.; Singer, I.
Lexicographical order, lexicographical index, and linear operators.
Linear Algebra Appl. 128 (1990), 65-95.

Martínez-Legaz, J. E.
On lower subdifferentiable functions.
Trends in mathematical optimization (Irsee, 1986), 197-232, Internat. Schriftenreihe Numer. Math., 84, Birkhäuser, Basel, 1988.
MathSciNet

Martínez-Legaz, J. E.; Singer, I.
The structure of hemispaces in Rn.
Linear Algebra Appl. 110 (1988), 117-179.

Martínez-Legaz, J. E.
Quasiconvex duality theory by generalized conjugation methods.
Optimization 19 (1988), no. 5, 603-652.

Martínez-Legaz, J. E.
Lexicographical order and duality in multiobjective programming.
European J. Oper. Res. 33 (1988), no. 3, 342-348.

Martínez-Legaz, J. E.; Singer, I.
Surrogate duality for vector optimization.
Numer. Funct. Anal. Optim. 9 (1987), no. 5-6, 547-568.

Martínez-Legaz, J. E.; Singer, I.
Lexicographical separation in Rn.
Linear Algebra Appl. 90 (1987), 147-163.

Martínez-Legaz, J. E.
Level sets and the minimal time function of linear control processes.
Numer. Funct. Anal. Optim. 9 (1987), no. 1-2, 105-129.

Martínez-Legaz, J. E.
Some new results on exact quasiconvex duality.
IX symposium on operations research. Part I. Sections 1-4 (Osnabrück, 1984), 47-62, Methods Oper. Res., 49, Athenäum/Hain/Hanstein, Königstein, 1985.

MathSciNet

Martínez-Legaz, J. E.
Lexicographical order, inequality systems and optimization.
System modelling and optimization (Copenhagen, 1983), 203-212, Lecture Notes in Control and Inform. Sci., 59, Springer, Berlin, 1984.

Martínez-Legaz, J. E.
A new approach to symmetric quasiconvex conjugacy.
Selected topics in operations research and mathematical economics (Karlsruhe, 1983), 42-48, Lecture Notes in Econom. and Math. Systems, 226, Springer, Berlin, 1984.
MathSciNet

Martinez-Legaz, J. E.
A generalized concept of conjugation.
Optimization: theory and algorithms (Confolant, 1981), 45-59, Lecture Notes in Pure and Appl. Math., 86, Dekker, New York, 1983.

MathSciNet

Martinez-Legaz, J. E.
Exact quasiconvex conjugation.
Z. Oper. Res. Ser. A-B 27 (1983), no. 7, A257–A266.

Martinez-Legaz, J. E.
Conjugation associated with a graph. (Spanish)
Proceedings of the ninth Spanish-Portuguese conference on mathematics, 2 (Salamanca, 1982),
837–839, Acta Salmanticensia. Ciencias, 46, Univ. Salamanca, Salamanca, 1982.