An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes

Mathematics

Aleksandar Valjarević¹  Julija Mladenović²  Dejan Ilić³  Milena J. Petrović⁴  Dragana Valjarević⁴ 

[1] Faculty of Geography, University of Belgrade, Studentski Trg 3/III, 11000 Belgrade, Serbia;Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Belgrade, Serbia;Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18106 Niš, Serbia;Faculty of Sciences and Mathematics, University of Pristina in Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia;

关键词: gradient descent;    line search;    gradient descent methods;    quasi-Newton method;    convergence rate;   

DOI  :  10.3390/math10020259

来源: DOAJ

【 摘 要 】

We propose an improved variant of the accelerated gradient optimization models for solving unconstrained minimization problems. Merging the positive features of either double direction, as well as double step size accelerated gradient models, we define an iterative method of a simpler form which is generally more effective. Performed convergence analysis shows that the defined iterative method is at least linearly convergent for uniformly convex and strictly convex functions. Numerical test results confirm the efficiency of the developed model regarding the CPU time, the number of iterations and the number of function evaluations metrics.

【 授权许可】

Unknown