مقایسهٔ روش‌ها

	بهینه‌سازی استوار	بهینه‌سازی تصادفی
حوزه	بهینه‌سازی	بهینه‌سازی
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	1970s theoretical roots; modern tractable form from late 1990s–2004	1951 (SGD); 2014 (Adam)
پدیدآور	Ben-Tal, El Ghaoui & Nemirovski (seminal book, 2009); Bertsimas & Sim (tractable polyhedral formulation, 2004)	—
نوع	Mathematical programming framework	Gradient-based iterative optimization
منبع بنیادین	Ben-Tal, A., El Ghaoui, L. & Nemirovski, A. (2009). Robust Optimization. Princeton University Press. ISBN: 9780691143682	Robbins, H. & Monro, S. (1951). A Stochastic Approximation Method. Annals of Mathematical Statistics, 22(3), 400-407.
نام‌های دیگر	minimax optimization, worst-case optimization, Gürbüz Optimizasyon (Robust Optimization)	Stokastik Optimizasyon (SGD & Varyantları), stochastic gradient descent, SGD, Adam
مرتبط	5	3
خلاصه	Robust optimization is a mathematical programming framework, formalised by Ben-Tal and Nemirovski in the late 1990s and made broadly tractable by Bertsimas and Sim (2004), that finds decisions guaranteed to perform acceptably under every scenario within a predefined uncertainty set — rather than assuming parameter values are known exactly. Instead of optimising for a single expected outcome, it minimises the worst-case objective across all plausible realisations of uncertain data.	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.