An improved search direction based on algebraic equivalent transformation technique for convex quadratic optimization
نویسندگان
1 Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Setif 1 University-Ferhat Abbas, Setif, 19000, Algeria.
2 Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Setif 1 University-Ferhat Abbas, Setif, 19000, Algeria.
3 Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Setif 1 University-Ferhat Abbas, Setif, 19000, Algeria.
doi
10.22067/ijnao.2025.94069.1670چکیده
This work presents an improved interior point algorithm with full Newton step for convex quadratic optimization. Based on the technique of algebraic equivalent transformation, we first propose a new search direction for convex quadratic optimization with the aim of improving the algorithmic complexity of the proposed algorithm. We then perform a complete theoretical study of convergence and complexity, proving that our algorithm is well-defined, converge quadratically and achieves the best known polynomial complexity bounds established for primal-dual interior point methods. Following this, we conduct comparative numerical tests to evaluate the efficiency of the algorithm. The theoretical and numerical results are encouraging and clearly confirm our purpose.
