# Numerical Methods for Convex Quadratic Programming with Nonnegative Constraints

### 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

### References

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.

*Journal of Progressive Research in Mathematics*,

*20*(1), 39-48. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/2194

Copyright (c) 2023 Journal of Progressive Research in Mathematics

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.