手法を比較

	非線形計画法	動的計画法
分野	最適化	最適化
系統	Process / pipeline	Process / pipeline
提唱年	2006	1957
提唱者	Jorge Nocedal & Stephen Wright	Richard Bellman
種類	Continuous mathematical optimization	Exact combinatorial optimization via recursive decomposition
原典	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
別名	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama
関連	3	3
概要	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.