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| 二次計画法 (QP)× | 線形計画法× | |
|---|---|---|
| 分野 | 最適化 | 最適化 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1956 | 1947 |
| 提唱者≠ | Marguerite Frank & Philip Wolfe | George B. Dantzig |
| 種類≠ | Constrained mathematical optimization | 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. DOI ↗ | 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 | LP, linear optimization, Doğrusal Programlama (LP) |
| 関連≠ | 2 | 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. | 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. |
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