مقایسهٔ روش‌ها

	برنامه‌ریزی غیرخطی	بهینه‌سازی تصادفی
حوزه	بهینه‌سازی	بهینه‌سازی
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	2006	1951 (SGD); 2014 (Adam)
پدیدآور	Jorge Nocedal & Stephen Wright	—
نوع	Continuous mathematical optimization	Gradient-based iterative optimization
منبع بنیادین	Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer. ISBN: 978-0-387-30303-1	Robbins, H. & Monro, S. (1951). A Stochastic Approximation Method. Annals of Mathematical Statistics, 22(3), 400-407.
نام‌های دیگر	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama	Stokastik Optimizasyon (SGD & Varyantları), stochastic gradient descent, SGD, Adam
مرتبط	3	3
خلاصه	Nonlinear programming (NLP) is a branch of mathematical optimization concerned with problems in which the objective function or at least one constraint is nonlinear. Formalized comprehensively by Jorge Nocedal and Stephen Wright in their seminal 2006 text, NLP encompasses gradient-based algorithms — including sequential quadratic programming (SQP), interior-point methods, and quasi-Newton approaches — for finding locally or globally optimal solutions to continuous decision problems arising across engineering, economics, and the physical sciences.	Stochastic optimization is a family of iterative methods that minimize an objective function by computing gradients on randomly sampled subsets of data — mini-batches — rather than on the entire dataset at once. Pioneered by Robbins and Monro in 1951 as stochastic approximation, the approach became the standard engine for training large-scale machine-learning models through variants such as SGD with momentum, AdaGrad, RMSProp, and Adam.