An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes
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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
Кључне речи:
gradient descent / line search / gradient descent methods / quasi-Newton method / convergence rateИзвор:
Mathematics, 2022, 10, 2, 259-Издавач:
- Basel : MDPI
DOI: 10.3390/math10020259
ISSN: 2227-7390
WoS: 000746003900001
Scopus: 2-s2.0-85123003839
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Geografski fakultetTY - JOUR AU - Petrović, Milena AU - Valjarević, Dragana AU - Ilić, Dejan AU - Valjarević, Aleksandar AU - Mladenović, Julija PY - 2022 UR - http://gery.gef.bg.ac.rs/handle/123456789/1185 AB - 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 PB - Basel : MDPI T2 - Mathematics T1 - An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes VL - 10 IS - 2 SP - 259 DO - 10.3390/math10020259 ER -
@article{ author = "Petrović, Milena and Valjarević, Dragana and Ilić, Dejan and Valjarević, Aleksandar and Mladenović, Julija", year = "2022", abstract = "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", publisher = "Basel : MDPI", journal = "Mathematics", title = "An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes", volume = "10", number = "2", pages = "259", doi = "10.3390/math10020259" }
Petrović, M., Valjarević, D., Ilić, D., Valjarević, A.,& Mladenović, J.. (2022). An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes. in Mathematics Basel : MDPI., 10(2), 259. https://doi.org/10.3390/math10020259
Petrović M, Valjarević D, Ilić D, Valjarević A, Mladenović J. An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes. in Mathematics. 2022;10(2):259. doi:10.3390/math10020259 .
Petrović, Milena, Valjarević, Dragana, Ilić, Dejan, Valjarević, Aleksandar, Mladenović, Julija, "An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes" in Mathematics, 10, no. 2 (2022):259, https://doi.org/10.3390/math10020259 . .