TY  - JOUR
T1  - Exponential-Quadratic-Logarithmic Composite Function Optimization In Positive Domains: Leveraging Multiplicative Calculus In Gradient Descent Algorithms
AU  - Kıymık, Erkan
AU  - Öztürk, Ali Emre
PY  - 2024
DA  - June
Y2  - 2024
DO  - 10.29132/ijpas.1467644
JF  - International Journal of Pure and Applied Sciences
PB  - Munzur Üniversitesi
WT  - DergiPark
SN  - 2149-0910
SP  - 209
EP  - 227
VL  - 10
IS  - 1
LA  - en
AB  - This work investigates the integration of multiplicative calculus into gradient descent algorithms, including Adaptive Gradient algorithm (AdaGrad), Root Mean Squared Propagation (RMSProp), Nesterov Accelerated Gradient (NAG), and Momentum, to optimize exponential-quadratic-logarithmic composite functions with the positivity constrained. This research, conducted across five scenarios within the Constrained and Unconstrained Testing Environment (CUTEst), compares these multiplicative methods with their classical counterparts under a variety of constraints environments such as bounded, quadratic, and other types, and unconstrained environments. The results demonstrate the significant superiority of multiplicative-based algorithms, especially in unconstrained and bounded constrained scenarios, and demonstrate their potential for complex optimization tasks. Statistical analysis supports the observed performance advantages, indicating significant opportunities for optimization strate-gies in positive domains.
KW  - Gradient Descent
KW  - Optimization
KW  - Multiplicative calculus
KW  - Machine Learning
KW  - Composite Functions
KW  - Non-newtonian Calculus
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UR  - https://doi.org/10.29132/ijpas.1467644
L1  - https://dergipark.org.tr/tr/download/article-file/3859277
ER  -