Efficient Quadratic Programming Optimization via Staged Computational Procedures: Unconstrained Minimization and Constraint Exploration

Efficient Quadratic Programming Optimization via Staged Computational Procedures

Abstract

In this paper, we present a computational framework for finding optimal solutions to quadratic programming problems. Our computational process is divided into three steps. Initially, we derive unconstrained minimization of the quadratic programming problem by solving simultaneous equations involving objective function derivatives and confirming its feasibility. Using this discovered point, we identify the violated constraints and direct our search to these specific constraints. The next stage defines the process for determining the unconstrained point on each active constraint violated by the objective function's optimal point. Moving on to the next stage, we use the constraint exploration technique to systematically seek the optimal constrained point at the intersections of two or more violated active constraints as candidates for the optimal solution. The feasibility of the unconstrained point is systematically checked at each level. If the unconstrained point is deemed feasible, then the optimal solution is obtained, and the optimal value of the objective function is found.