Efficient Optimization of Integer Quadratic Programming Through State Variables Reduction Using Separable Algorithms

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Mintu Kumar Sah , Neha Varma

Abstract

Introduction: This paper tackles significant challenges in nonlinear programming and integer quadratic programming problems (IQPPs), presenting innovative solution methodologies. It introduces advanced decision-variable reduction techniques for IQPPs, optimizing solutions by minimizing state variables. The study establishes necessary and sufficient conditions for IQPPs and develops strategies to identify dominated terms in problem formulations. Variable reduction is further refined by analyzing problem data and upper bounds, enabling certain variables to be fixed at zero. A detailed computational analysis highlights the efficiency of these methods across various IQPP scenarios. Additionally, the paper provides insights into separable IQPPs, offering a streamlined framework to enhance comprehension and facilitate intuitive problem-solving. MATLAB-based simulations and graphical representations underscore the practical applicability and robustness of the proposed techniques.

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