Numerical Methods for Convex Quadratic Programming with Nonnegative Constraints
Keywords:
Quadratic Programming; Ordinary Differential Equations; the Modified Implicit Euler Method
Abstract
This paper deals with some problems in numerical simulation for convex quadratic programming with nonnegative constraints. For systems of ordinary differential equations which derived from the above mentioned problem, we construct a kind of new numerical method: the modified implicit Euler method. Under some restrictions for step-size, we obtained the numerical solution which satisfied with the termination condition. Compared with the classical Matlab command ODE23, the new method has ideal computation cost.
Downloads
Download data is not yet available.
References
[1] F. Sha, L.K. Saul, D.D. Lee. Multiplicative updates for nonnegative programming in support vector
machines. Advances in Neural Information Processing Systems, 15:1041-1048, 2003.
[2] M.V. Bulatov, A.V. Tygliyan, S.S. Filippov. A class of one-step one-stage methods for stiff systems of
ordinary differential equations. Computational Mathematics and Mathematical Physics, 51(7): 1167-
1180, 2011.
[3] H. Zheng, W. Han. On some discretization methods for solving a linear matrix ordinary differential
equation. J. Math. Chem., 49: 1026-1041, 2011.
[4] V.M. Abdullaev, K.R. Aida-Zade. Numerical method of solution to loaded nonlocal boundary value
problems for ordinary differential equations. Computational Mathematics and Mathematical Physics,
54(7): 1096-1109, 2014.
[5] H. Liang, M.Z. Liu, Z.W. Yang. Stability analysis of Runge-Kutta methods for systems u′(t) = Lu(t) +Mu([t]). Applied Mathematics and Computation, 228: 463-476, 2014.
[6] M. Saravi, E. Babolian, R. England, et al. System of linear ordinary differential and differential-algebraic
equations and pseudo-spectral method. Computers and Mathematics with Applications, 59: 1524-1531,
2010.
[7] M. Khanamiryan. Quadrature methods for highly oscillatory linear and non-linear systems of ordinary
differential equations: part I. BIT Numerical Mathematics, 48: 743-761, 2008.
[8] M. Khanamiryan. Quadrature methods for highly oscillatory linear and non-linear systems of ordinary
differential equations: part II. BIT Numerical Mathematics, 52: 383-405, 2012.
[9] L. Gimena, P. Gonzaga, F.N. Gimena. Boundary equations in the finite transfer method for solving
differential equation systems. Applied Mathematical Modelling, 38: 2648-2660, 2014.
[10] Z. Jackiewicz. Construction and implementation of general linear methods for ordinary differential
equations: A Review. Journal of Scientific Computing, 25(1/2): 29-49, 2005.
[11] H. Zhang, A. Sandu, S. Blaise. Partitioned and implicit-explicit general linear methods for ordinary
differential equations. Journal of Scientific Computing, 61: 119-144, 2014.
[12] M. Qayyum, Q. Fatima. Solutions of stiff systems of ordinary differential equations using residual power
series method. Journal of Mathematics, 2022: 1-7, 2022.
[13] F.M. Burrell, P.E. Warwick, I.W. Croudace, W.S. Walters. Development of a numerical simulation
method for modelling column breakthrough from extraction chromatography resins. Analyst, 146: 4049-
4065, 2021.
[14] R. Abu-Gdairi, S. Hasan, S. Al-Omari, et al. Attractive multistep reproducing kernel approach for
solving stiffness differential systems of ordinary differential equations and some error analysis. Computer
Modeling in Engineering and Sciences, 130(1): 299-313, 2022.
[15] L.Z. Liao, H.D. Qi, L.Q. Qi. Neurodynamical optimization. JOGO, 28:175-195, 2004.
[16] H.W. Yue. First-order affine scaling continuous method for convex quadratic programming. Hong Kong
Baptist University, 2014.
machines. Advances in Neural Information Processing Systems, 15:1041-1048, 2003.
[2] M.V. Bulatov, A.V. Tygliyan, S.S. Filippov. A class of one-step one-stage methods for stiff systems of
ordinary differential equations. Computational Mathematics and Mathematical Physics, 51(7): 1167-
1180, 2011.
[3] H. Zheng, W. Han. On some discretization methods for solving a linear matrix ordinary differential
equation. J. Math. Chem., 49: 1026-1041, 2011.
[4] V.M. Abdullaev, K.R. Aida-Zade. Numerical method of solution to loaded nonlocal boundary value
problems for ordinary differential equations. Computational Mathematics and Mathematical Physics,
54(7): 1096-1109, 2014.
[5] H. Liang, M.Z. Liu, Z.W. Yang. Stability analysis of Runge-Kutta methods for systems u′(t) = Lu(t) +Mu([t]). Applied Mathematics and Computation, 228: 463-476, 2014.
[6] M. Saravi, E. Babolian, R. England, et al. System of linear ordinary differential and differential-algebraic
equations and pseudo-spectral method. Computers and Mathematics with Applications, 59: 1524-1531,
2010.
[7] M. Khanamiryan. Quadrature methods for highly oscillatory linear and non-linear systems of ordinary
differential equations: part I. BIT Numerical Mathematics, 48: 743-761, 2008.
[8] M. Khanamiryan. Quadrature methods for highly oscillatory linear and non-linear systems of ordinary
differential equations: part II. BIT Numerical Mathematics, 52: 383-405, 2012.
[9] L. Gimena, P. Gonzaga, F.N. Gimena. Boundary equations in the finite transfer method for solving
differential equation systems. Applied Mathematical Modelling, 38: 2648-2660, 2014.
[10] Z. Jackiewicz. Construction and implementation of general linear methods for ordinary differential
equations: A Review. Journal of Scientific Computing, 25(1/2): 29-49, 2005.
[11] H. Zhang, A. Sandu, S. Blaise. Partitioned and implicit-explicit general linear methods for ordinary
differential equations. Journal of Scientific Computing, 61: 119-144, 2014.
[12] M. Qayyum, Q. Fatima. Solutions of stiff systems of ordinary differential equations using residual power
series method. Journal of Mathematics, 2022: 1-7, 2022.
[13] F.M. Burrell, P.E. Warwick, I.W. Croudace, W.S. Walters. Development of a numerical simulation
method for modelling column breakthrough from extraction chromatography resins. Analyst, 146: 4049-
4065, 2021.
[14] R. Abu-Gdairi, S. Hasan, S. Al-Omari, et al. Attractive multistep reproducing kernel approach for
solving stiffness differential systems of ordinary differential equations and some error analysis. Computer
Modeling in Engineering and Sciences, 130(1): 299-313, 2022.
[15] L.Z. Liao, H.D. Qi, L.Q. Qi. Neurodynamical optimization. JOGO, 28:175-195, 2004.
[16] H.W. Yue. First-order affine scaling continuous method for convex quadratic programming. Hong Kong
Baptist University, 2014.
Published
2023-03-05
How to Cite
Wang, Q. (2023). Numerical Methods for Convex Quadratic Programming with Nonnegative Constraints. Journal of Progressive Research in Mathematics, 20(1), 39-48. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/2194
Issue
Section
Articles
Copyright (c) 2023 Journal of Progressive Research in Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
