Year 2015,
Volume: 36 Issue: 5, 86 - 102, 20.08.2015
Abstract
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
References
- 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
Year 2015,
Volume: 36 Issue: 5, 86 - 102, 20.08.2015
Abstract
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.
References
- 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
There are 9 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Natural Sciences Research Article |
| Authors | |
| Publication Date | August 20, 2015 |
| Published in Issue | Year 2015 Volume: 36 Issue: 5 |