TITLE:
Further Numerical Results for a New Lagrange Method for Solving Convex Quadratic Optimization Problems
AUTHORS:
John Avoka, Stephen B. Twum, Christian J. Etwire
KEYWORDS:
Convex Quadratic Programming, Lagrangian Function, Lagrange Multipliers, Optimality Condition, Subsidiary Constraint Equations
JOURNAL NAME:
Open Journal of Optimization,
Vol.15 No.3,
September
30,
2026
ABSTRACT: The work reported in this paper is a sequel to an earlier paper of the authors in which a modified classical Lagrange Multiplier method was used to solve merely small-sized convex quadratic optimization problems, where hand computation was possible. In the current work, the authors demonstrate the utility of the new method in solving medium to large sized convex quadratic optimization problems for which hand computations are impossible, or cumbersome. The modified version of the Lagrange method was numerically analyzed against the classical Lagrange method using performance measures of: solution output, run-time, number of iterations needed to converge, and number of function evaluations in solving a given convex quadratic optimization problem. The hypothetically constructed problems which were run in MATLAB produced results that showed that, generally, the modified version of the Lagrange method was as good as, or out-performed, the latter in the performance indicators.