Summary
In this paper one generalizes various types of constrained extremism, keeping the Lagrange or Kuhn-Tucker multipliers rule. The context which supports this development is the nonholonomic optimization theory which requires a holonomic or nonholonomic objective function subject to nonholonomic or holonomic constraints. We refined such a problem using two new ideas: the replacement of the point or velocity constraints by a curve selector, and the geometrical interpretation of the Lagrange and Kuhn-Tucker parameters. The classical optimization theory is recovered as a particular case of extremism constrained by a curve selector.
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References
C. Udrişte and O. Dogaru. Mathematical Programming Problems with Nonholonomic Constraints. Seminarul de Mecanică, Univ. of Timişoara, Fac. de Ştiinţe ale Naturii, vol. 14, 1988.
C. Udrişte and O. Dogaru. Extrema with nonholonomic constraints. Buletinul Institutului Politehnic Bucureşti, Seria Energetică, 50:3–8, 1988.
C. Udrişte and O. Dogaru. Extreme conditionate pe orbite. Sci. Bull., 51:3–9, 1991.
C. Udrişte and O. Dogaru. Convex nonholonomic hypersurfaces. In: G. Rassias (ed), Math. Heritage of C.F. Gauss, World Scientific, pp. 769–784, 1991.
C. Udrişte, O. Dogaru and I. Ţevy. Sufficient conditions for extremum on differentiable manifolds. Sci. Bull. P.I.B., Elect. Eng., 53(3–4):341–344, 1991.
C. Udrişte, O. Dogaru and I. Ţevy. Extremum points associated with Pfaff forms. Tensor, N.S., 54:115–121, 1993.
C. Udrişte, O. Dogaru and I. Ţevy. Open problems in extrema theory. Sci. Bull. P.U.B., Series A, 55(3–4):273–277, 1993.
O. Dogaru, I. Ţevy and C. Udrişte. Extrema constrained by a family of curves and local extrema. JOTA,97(3):605–621, 1998.
C. Udrişte, O. Dogaru and I. Ţevy. Extrema constrained by a Pfaff system. In: T. Gill, K. Liu, and E. Trell (Eds.), Fundamental Open Problems in Science at the End of Millenium, vol. I–III, Hadronic Press, Inc., Palm Harbor, FL, pp. 559–573, 1999.
O. Dogaru and I. Ţevy. Extrema constrained by a family of curves. Proc. Workshop on Global Analysis, Differential Geometry and Lie Algebras, 1996, Gr. Tsagas (Ed.), Geometry Balkan Press, pp. 185–195, 1999.
O. Dogaru and V. Dogaru. Extrema constrained by Ck curves. Balkan J. Geometry and Its Applications, 4(1):45–52, 1999.
C. Udrişte. Geometric Dynamics. Kluwer Academic Publishers, 2000.
C. Udrişte, O. Dogaru and I. Ţevy. Extrema with Nonholonomic Constraints. Monographs and Textbooks 4, Geometry Balkan Press, 2002.
C. Udrişte, O. Dogaru, M. Ferrara, I. Ţevy. Pfaff inequalities and semi-curves in optimum problems. In: G.P. Crespi, A. Guerragio, E. Miglierina, M. Rocca (Eds.), Recent Advances in Optimization, DATANOVA, pp.191–202, 2003.
C. Udrişte, O. Dogaru, M. Ferrara, I. Ţevy. Extrema with constraints on points and/or velocities. Balkan J. Geometry and Its Applications, 8(1):115–123, 2003.
T. Otsuki. General connections. Math. J. Okayama Univ. 32:227–242, 1990.
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Udrişte, C., Dogarul, O., Ferrara, M., Ţevy, I. (2006). Nonholonomic Optimization. In: Seeger, A. (eds) Recent Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28258-0_8
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DOI: https://doi.org/10.1007/3-540-28258-0_8
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