Öz
In this work, we …rst de…ne the Hessian form of a hypersurface,then we relate it to the Second Fundamental form of the hypersurface.In the remaining part of this work, we use these formulas to show, howto evaluate the local and restricted extreme values of the hypersurfaceaccording to a given hyperplane
Anahtar Kelimeler
Hypersurface gradient covariant derivative Hessianform second fundamental form extremum
Kaynakça
- Jonh A. Thorpe. Elementary Topics in Di¤erential Geometry. Springer- Verlag, New York. 1979. pp. 95-100
- Stephen Nash, Ariela Sofer, Linear and Nonlinear Programming. The McGraw-Hill Companies Inc., New York, 1996. pp: 338-650
- Mokhtrar S. Bazaran, C.M. Shetty. Nonlinear Programming Theory and Algorithms. John Wiley & Sons, New York, 1979. pp:252
- Jafolich C. Arya, Robin W. Lardner. Mathematical Analysis, Prentice Hall, Inc. New York 1993 pp :768
- Boothby M. William. An Introduction to Di¤erentiable Manifolds and Riemannian Geometry Academic Press. New York, 1995. pp:363-369
- Kobayashi S. , Nomizu K. Foundations of Di¤erential Geometry. vol:2. Interscience Publishers, New York, 1967. pp:40-46
- A. A. Groenwold. Positive de…nite separable quadratic programs for non-convex problems, Structural Multidisciplinary Optimization, (2012) 46:795–802, DOI 10.1007/s00158-012-0810-8
- Zh. B. Zhu, J. B. Jian. An Improved Feasible QP-free Algorithm for Inequality Constrained Optimization, Acta Mathematica Sinica, English Series, Dec., 2012, Vol. 28, No. 12, pp. 2475–2488, DOI: 10.1007/s10114- 012-0561-x
- M. Petrache, Meaning of the Hessian of a function in a critical point, February 1, 2012, http://www.math.ethz.ch/~petrache/hessian.pdf
Öz
Bu çalışmada, önce bir hiperyüzeyin Hessian formu tanımlandı, sonra bu hiperyüzeylerin İkinci Temel formu ile ilişkilendirildi. Çalışmanın devamında, elde edilen formuller ile lokal ve sınırlandırılmamış ekstirim değerlerin nasıl değerlendirilebileceği gösterildi.
Anahtar Kelimeler
Hiperyüzey gradient kovaryant türev Hessianform ikinci temel form ekstremum
Kaynakça
- Jonh A. Thorpe. Elementary Topics in Di¤erential Geometry. Springer- Verlag, New York. 1979. pp. 95-100
- Stephen Nash, Ariela Sofer, Linear and Nonlinear Programming. The McGraw-Hill Companies Inc., New York, 1996. pp: 338-650
- Mokhtrar S. Bazaran, C.M. Shetty. Nonlinear Programming Theory and Algorithms. John Wiley & Sons, New York, 1979. pp:252
- Jafolich C. Arya, Robin W. Lardner. Mathematical Analysis, Prentice Hall, Inc. New York 1993 pp :768
- Boothby M. William. An Introduction to Di¤erentiable Manifolds and Riemannian Geometry Academic Press. New York, 1995. pp:363-369
- Kobayashi S. , Nomizu K. Foundations of Di¤erential Geometry. vol:2. Interscience Publishers, New York, 1967. pp:40-46
- A. A. Groenwold. Positive de…nite separable quadratic programs for non-convex problems, Structural Multidisciplinary Optimization, (2012) 46:795–802, DOI 10.1007/s00158-012-0810-8
- Zh. B. Zhu, J. B. Jian. An Improved Feasible QP-free Algorithm for Inequality Constrained Optimization, Acta Mathematica Sinica, English Series, Dec., 2012, Vol. 28, No. 12, pp. 2475–2488, DOI: 10.1007/s10114- 012-0561-x
- M. Petrache, Meaning of the Hessian of a function in a critical point, February 1, 2012, http://www.math.ethz.ch/~petrache/hessian.pdf
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Fen Bilimleri Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 20 Ağustos 2015 |
| Yayımlandığı Sayı | Yıl 2015 Cilt: 36 Sayı: 5 |