방법 비교

	비선형 계획법	동적 계획법	확률적 최적화
분야	최적화	최적화	최적화
계열	Process / pipeline	Process / pipeline	Process / pipeline
기원 연도	2006	1957	1951 (SGD); 2014 (Adam)
창시자	Jorge Nocedal & Stephen Wright	Richard Bellman	—
유형	Continuous mathematical optimization	Exact combinatorial optimization via recursive decomposition	Gradient-based iterative optimization
원전	Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer. ISBN: 978-0-387-30303-1	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Robbins, H. & Monro, S. (1951). A Stochastic Approximation Method. Annals of Mathematical Statistics, 22(3), 400-407.
별칭	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	Stokastik Optimizasyon (SGD & Varyantları), stochastic gradient descent, SGD, Adam
관련	3	3	3
요약	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.	Dynamic Programming (DP) is an exact optimization technique introduced by Richard Bellman in 1957 for solving multi-stage decision problems. It decomposes a complex problem into simpler, overlapping subproblems, solves each subproblem once, and stores the results to avoid redundant computation. Grounded in the Principle of Optimality, DP guarantees globally optimal solutions whenever the problem exhibits overlapping subproblems and optimal substructure.	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.