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<p>This paper suggests an iterative method for optimizing a Quadratic Programming Problem, constrained with a set of Linear Inequalities (less than type), regardless of the nature of the square matrix (<i>B</i>) within the objective function. To reach the global solution the entire travel is devised with a set of specially designed (<i>n – m</i>) (&gt; <i>m</i>) vectors while incorporating a Resultant Vector Ascent Method (where&#xa0;<i>n&#xa0;</i>and&#xa0;<i>m&#xa0;represent the</i> number of variables (including slack variables) and constraints). These vectors are <i>located</i> in the null space of the <Emphasis Type="BoldItalic">constraint</Emphasis> matrix and half of them are dependent on the Eigenvectors of <i>B</i>. The prescribed movements can optimize the problem with a time complexity of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbf{O}\left[{\left({\varvec{n}}-{\varvec{m}}\right)}^{2}{[\left({\varvec{n}}-{\varvec{m}}\right)}^{2}+{{\varvec{n}}}^{2}]\right]\)</EquationSource> </InlineEquation> and <i>without causing a looping problem during degeneracy</i>.</p>

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Optimizing a Linearly Constrained Quadratic Programming Problem Using Eigen-Value Decomposition and Resultant Vector Ascent Method

  • 期刊论文

  • 发表日期：

    2025年10月18日

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  • Subhadip Sarkar

摘要

This paper suggests an iterative method for optimizing a Quadratic Programming Problem, constrained with a set of Linear Inequalities (less than type), regardless of the nature of the square matrix (B) within the objective function. To reach the global solution the entire travel is devised with a set of specially designed (n – m) (> m) vectors while incorporating a Resultant Vector Ascent Method (where n and m represent the number of variables (including slack variables) and constraints). These vectors are located in the null space of the constraint matrix and half of them are dependent on the Eigenvectors of B. The prescribed movements can optimize the problem with a time complexity of \(\mathbf{O}\left[{\left({\varvec{n}}-{\varvec{m}}\right)}^{2}{[\left({\varvec{n}}-{\varvec{m}}\right)}^{2}+{{\varvec{n}}}^{2}]\right]\) and without causing a looping problem during degeneracy.