C^1'1 vector optimization problems and Riemann derivatives

• Autorzy: Ginchev I. , Guerraggio A. , Rocca M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we introduce a generalized second-order Riemann-type derivative for C^1'1 vector functions and use it to establish necessary and sufficient optimality conditions for vector optimization problems. We show that, these conditions are stronger than those obtained by means of the second-order subdinerential in Clarke sense considered in Guerraggio, Luc (2001) and also to some extent than those obtained in Guerraggio, Luc, Minh (2001).

Słowa kluczowe

EN

vector optimization; Riemann-type directional derivatives; second-order optimality conditions

PL

optymalizacja wektorowa; pochodna kierunkowa typu Riemanna; warunek optymalności dwuwskaźnikowy

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2004
• Tom: Vol. 33, no 2
• Strony: 259--273
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Ginchev I.

• Technical University of Varna Department of Mathematics Studentska Str.9010 Varna, Bulgaria

autor

Guerraggio A.

• ”Bocconi” University of MilanInstitute of Quantitative Methodsviale Isonzo, 25, 20135 Milano, Italy

autor

Rocca M.

• University of Insubria Department of Economics via Ravasi, 2, 21100 Varese, Italy

Bibliografia

• Ash, J.M. (1967) Generalizations of the Riemann derivative.Trans. Amer. Math. Soc. 126, 181-199.
• Ash, J.M. (1985) Very generalized Riemann derivatives. Real Anal. Exchange 12, 10-29.
• Ginchev, I. and Guerraggio, A. (1998) Second order optimality conditionsin nonsmooth unconstrained optimization. Pliska Stud. Math. Bulgar.12,39-50.
• Guerraggio, A. and Luc, D.T. (2001) Optimality conditions for C1,1vector optimization problems. J. Optim. Theory Appl.109, 615-629.
• Guerraggio, A. and Luc, D.T. (2003) Optimality conditions for C1,1constrained multiobjective problems. J. Optim. Theory Appl.116, 117-129.
• Guerraggio, A., Luc, D.T. and Minh, N.B. (2001) Second-order optimality conditions for C1multiobjective programming problems. Acta Math. Vietnam 26, 257–268.
• Hiriart-Urruty, J.B., Strodiot, J.J. and ien Hguyen, V. (1984)Generalized Hessian matrix and second-order optimality conditions for problems with C1,1 data. Appl. Math. Opt.11, 43-56.
• Jeyakumar, V. and Luc, D.T. (1998) Approximate Jacobian matrices fornonsmooth continuous maps and C1-optimization. SIAM J. Control Optim. 36, 1815-1832.
• Klatte, D. and Tammer, K. (1988) On the second order sufficient conditions to perturbed C1,1 optimization problems. Optimization.19, 169-180.
• La Torre, D. and Rocca, M. (2001/02) A characterization of Ck, 1f unctions. Real Anal. Exchange 27, 515-534.
• Luc, D.T. (1989) Theory of Vector Optimization. Springer Verlag, Berlin.
• Luc, D.T. (1995) Taylor’s formula for Ck,1 functions. SIAM J. Optim. 5, 659-669.
• Luc, D.T. and Schaible, S. (1996) Generalized monotone nonsmooth maps. J. Convex Anal. 3, 195-205.
• Marcinkiewicz, J. and Zygmund, A. (1936) On the differentiability of functions and summability of trigonometrical series. Fund. Math. 26, 1-43.
• Riemann, B. (1892) Uber die darstelbarkeit einer funktion durch eine trigonometrische reihe. Ges. Werke, 2. Aufl., Leipzig, 227-271.
• Yang, X.Q. andJ eyakumar, V. (1992) Generalized second-order directional derivatives and optimization with C1,1 functions. Optimization 26, 165-185.
• Yang, X.Q. (1993) Second-order conditions in C1,1 optimization with applications. Numer. Funct. Anal. Optim.14, 621-632.
• Yang, X.Q. (1994) Generalized second-order derivatives and optimality conditions. Nonlinear Anal. 23, 767-784.
• Zygmund, A. (1959) Trigonometric Series.Cambridge.