مقایسهٔ روش‌ها

	بهینه‌سازی محدب	بهینه‌سازی تصادفی
حوزه	بهینه‌سازی	بهینه‌سازی
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	2004	1951 (SGD); 2014 (Adam)
پدیدآور	Stephen Boyd & Lieven Vandenberghe	—
نوع	Mathematical optimization framework	Gradient-based iterative optimization
منبع بنیادین	Boyd, S., & Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press. ISBN: 978-0-521-83378-3	Robbins, H. & Monro, S. (1951). A Stochastic Approximation Method. Annals of Mathematical Statistics, 22(3), 400-407.
نام‌های دیگر	Convex Programming, Disciplined Convex Programming, Dışbükey Optimizasyon, Convex Mathematical Programming	Stokastik Optimizasyon (SGD & Varyantları), stochastic gradient descent, SGD, Adam
مرتبط	3	3
خلاصه	Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets. Formalized and popularized by Stephen Boyd and Lieven Vandenberghe in their landmark 2004 textbook, the framework unifies a wide family of problems — including linear programming, quadratic programming, semidefinite programming, and second-order cone programming — under a single theoretical roof. Its defining property is that any locally optimal solution is also globally optimal, making it tractable and reliable for engineering, statistics, machine learning, and operations research.	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.