Preferences help
enabled [disable] Abstract
Number of results
2015 | 128 | 2B | B-213-B-214
Article title

SVD Augmented Gradient Optimization

Title variants
Languages of publication
Solution time of nonlinear constrained optimization problem depends on the number of constraints, decision variables and conditioning of decision variables space. While the numbers of constraints and decision variables are external to the optimization procedure itself, one may try to affect the conditioning of the decision variables space within the self contained optimization module. This will directly affect the ratio of convergence of an iterative, gradient based optimization routine. Another opportunity for speedup of the solution process in case of quadratic objective function lies in the chance to eliminate the decision variables least affecting the objective function, and thus decrease the optimization problem size. Elimination of decision variables is based on the singular value decomposition of the objective function. Singular values showing up as a result of such procedure indicate that certain linear combinations of original decision variables do not affect the objective function, and thus may be eliminated from further deliberations. Also if near singular values are encountered as well, even deeper reduction of the optimization problem size is still possible, but at a cost in terms of final solution quality. An idea how to improve the conditioning of decision variables space, and limit the number of decision variables in case of quadratic objective function using singular value decomposition is presented in this paper. Results of computer tests performed during minimization of quadratic objective function and subject to quadratic constraints are enclosed and discussed.
  • Cracow University of Technology, Faculty of Civil Engineering, Kraków, Poland
  • [1] J. Orkisz, M. Pazdanowski, in: Proc. X PCCM, Świnoujście (Poland), 1991, p. 591
  • [2] G.W. Stewart, SIAM Rev. 35, 551 (1993)
  • [3] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran, Cambridge University Press, Cambridge 1992
  • [4] LAPACK Users' Guide, SIAM, 1999
  • [5] GNU Scientific Library Reference Manual, 3rd ed., Network Theory, 2009
  • [6] J.B. Martin, Plasticity - Fundamentals and General Results, MIT Press, 1975
  • [7] W. Cecot, J. Orkisz, in: Proc. COMPLAS V, Barcelona (Spain), 1997, p. 1879
  • [8] J. Orkisz, A. Harris, Theor. Appl. Fract. Mech. 9, 109 (1988)
  • [9] J. Orkisz, O. Orringer, M. Hołowiński, M. Pazdanowski, W. Cecot, Comput. Struct. 35, 397 (1990)
  • [10] M. Pazdanowski, Arch. Transport XXII, 319 (2010)
  • [11] J. Orkisz, M. Pazdanowski, in: The Finite Element Method in the 1990's, Eds. E. Onate, J. Periaux, A. Samuelsson, Springer Verlag, 1991, p. 621
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.