方法对比

	凸优化	线性规划	非线性规划
领域	优化	优化	优化
方法族	Process / pipeline	Process / pipeline	Process / pipeline
起源年份	2004	1947	2006
提出者	Stephen Boyd & Lieven Vandenberghe	George B. Dantzig	Jorge Nocedal & Stephen Wright
类型	Mathematical optimization framework	Mathematical programming / continuous optimization	Continuous mathematical optimization
开创性文献	Boyd, S., & Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press. ISBN: 978-0-521-83378-3	Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136	Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer. ISBN: 978-0-387-30303-1
别名	Convex Programming, Disciplined Convex Programming, Dışbükey Optimizasyon, Convex Mathematical Programming	LP, linear optimization, Doğrusal Programlama (LP)	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama
相关	3	4	3
摘要	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.	Linear programming (LP), pioneered by George B. Dantzig in 1947, is a mathematical method for finding the best value of a linear objective function — such as minimum cost or maximum profit — subject to a set of linear inequality and equality constraints. It is the foundational technique in operations research and underlies production planning, resource allocation, logistics, diet problems, and countless other decision-making scenarios across engineering, economics, and the natural sciences.	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.