手法を比較

	二次計画法 (QP)	凸最適化	線形計画法
分野	最適化	最適化	最適化
系統	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1956	2004	1947
提唱者	Marguerite Frank & Philip Wolfe	Stephen Boyd & Lieven Vandenberghe	George B. Dantzig
種類	Constrained mathematical optimization	Mathematical optimization framework	Mathematical programming / continuous optimization
原典	Frank, M., & Wolfe, P. (1956). An algorithm for quadratic programming. Naval Research Logistics Quarterly, 3(1–2), 95–110.	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
別名	QP Optimization, Quadratic Optimization, Convex Quadratic Programming, İkinci Dereceden Programlama	Convex Programming, Disciplined Convex Programming, Dışbükey Optimizasyon, Convex Mathematical Programming	LP, linear optimization, Doğrusal Programlama (LP)
関連	2	3	4
概要	Quadratic Programming (QP) is a class of constrained mathematical optimization in which the objective function is quadratic and the constraints are linear. Formalized by Frank and Wolfe (1956) through their gradient-based feasible-direction algorithm, QP is foundational in operations research, finance, machine learning, and engineering design wherever one must minimize a convex (or non-convex) quadratic cost subject to linear feasibility conditions.	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.