TITLE:
A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems
AUTHORS:
Twum B. Stephen, Avoka John, Christian J. Etwire
KEYWORDS:
Quadratic Programming, Lagrangian Function, Lagrange Multipliers, Optimality Conditions, Subsidiary Equations, Modified Lagrange Method
JOURNAL NAME:
Open Journal of Optimization,
Vol.13 No.1,
March
18,
2024
ABSTRACT: 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.