Author(s)

Twum B. Stephen¹, Avoka John², Christian J. Etwire¹

¹School of Mathematical Science, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Ghana.
²Department of Mathematics, University for Development Studies, Tamale, Ghana.

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

Quadratic Programming, Lagrangian Function, Lagrange Multipliers, Optimality Conditions, Subsidiary Equations, Modified Lagrange Method

Stephen, T. , John, A. and Etwire, C. (2024) A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems. Open Journal of Optimization, 13, 1-20. doi: 10.4236/ojop.2024.131001.