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Second-order optimality conditions in nonsmooth vector optimization

   | 24 févr. 2024
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Aggarwal, S. (1998) Optimality and duality in mathematical programming involving generalized convex functions. Ph.D. thesis, University of Delhi, Delhi. Search in Google Scholar

Aghezzaf, B. (2003) Second order mixed type duality in multiobjective programming problem. Journal of Mathematical Analysis and Applications 285, 97–106. Search in Google Scholar

Ahmad, I. and Husain, Z. (2006) Second order (F; α ρ d)-convexity and duality in multiobjective programming. Information Sciences 176, 3094–3103. Search in Google Scholar

Auslender, A. (1979) Penalty methods for computing points that satisfy second order necessary conditions. Mathematical Programming 17, 229–238. Search in Google Scholar

Ben-Tal, A. and Zowe, J. (1985) Directional derivatives in nonsmooth optimization. Journal of Optimization Theory and Applications 47, 483–490. Search in Google Scholar

Coladas, L., Li, Z. and Wang, S. (1994) Optimality conditions for multiobjective and nonsmooth minimisation in abstract spaces. Bulletin of Australian Mathematical Society 50, 205–218. Search in Google Scholar

Cominetti, R. and Correa, R. (1990) A generalized second-order derivative in nonsmooth optimization. SIAM Journal on Control and Optimization 28, 789-809. Search in Google Scholar

Demyanov, W.F. and Pevnyi, A.B. (1974) Expansion with Respect to a Parameter of the Extremal Values of Game Problems. USSR Computational Mathematics and Mathematical Physics 14, 33-45. Search in Google Scholar

Facchinei, F. and Lucidi, S. (1998) Convergence to Second Order Stationary Points in Inequality Constrained Optimization. Mathematics of Operations Research 23, 746—766. Search in Google Scholar

Flores-Bazan, F., Hadjisavvas, N. and Vera, C. (2007) An Optimal Alternative Theorem and Applications to Mathematical Programming. Journal of Global Optimization 37, 229–243. Search in Google Scholar

Giorgi, G. and Guerraggio, A. (1996) The notion of invexity in vector optimization: Smooth and nonsmooth case. In: J. P. Crouzeix, J. E. Martinez-Legaz and M. Volle (Eds), Generalized Convexity, Generalized Monotonicity: Recent Results. Nonconvex Optimization and Its Applications, 27, Kluwer Academic Publishers, Dordrecht, 389–401. Search in Google Scholar

Hanson, M.A. (1993) Second order invexity and duality in mathematical programming. Opsearch 30, 313–320. Search in Google Scholar

Kumar, P. and Sharma, B. (2017) Higher order e ciency and duality for multiobjective variational problem. Control and Cybernetics, 46, 137-145. Search in Google Scholar

Luenberger, D. G. and Ye, Y. (2008) Linear and Nonlinear Programmming. Springer, New York. Search in Google Scholar

Mangasarian, O.L. (1975) Second and higher-order duality in nonlinear programming. Journal of Mathematical Analysis and Applications 51, 607–620. Search in Google Scholar

Mishra, S.K. (1997) Second order generalized invexity and duality in mathematical programming. Optimization 42, 51–69. Search in Google Scholar

Mond, B. (1974) Second-order duality for nonlinear programs. Opsearch 11, 90–99. Search in Google Scholar

Mond, B. and Weir, T. (1981-1983) Generalized convexity and higher order duality. Journal of Mathematical Sciences, 16–18, 74–94. Search in Google Scholar

Nocedal, J. and Wright, S. J. (2006) Numerical Optimization. Springer, New York. Search in Google Scholar

Suneja, S. K., Sharma, S. and Vani (2008) Second-order duality in vector optimization over cones. Journal of Applied Mathematics and Informatics 26, 251–261. Search in Google Scholar

Yuan, G. X., Chang, K. W., Hsieh, C. J. and Lin, C. J. (2010) A Comparison of Optimization Methods and Software for Large-scale L1-regularized Linear Classification. Journal of Machine Learning Research 11, 3183–3234. Search in Google Scholar