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| 凸最適化× | 線形計画法× | |
|---|---|---|
| 分野 | 最適化 | 最適化 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 2004 | 1947 |
| 提唱者≠ | Stephen Boyd & Lieven Vandenberghe | George B. Dantzig |
| 種類≠ | Mathematical optimization framework | Mathematical programming / continuous optimization |
| 原典≠ | 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≠ | Convex Programming, Disciplined Convex Programming, Dışbükey Optimizasyon, Convex Mathematical Programming | LP, linear optimization, Doğrusal Programlama (LP) |
| 関連≠ | 3 | 4 |
| 概要≠ | 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. |
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