袁亞湘研究員學術報告之瞎子爬山與最優(yōu)化方法(編輯修改稿)
2025-01-19 15:15 本頁面
【文章內容簡介】 小人物 ?? 大人物 ? Hotelling(18851973) ： “ But we all know the world is nonlinear.‖ ? Von Neumann(19031957): ―Mr. Chairman, Mr Chairman, if the speaker doesn’t mind, I would like to reply for him. The speaker titled his talk `linear programming’ and carefully stated his axioms. If you have an application that satisfies the axioms, well use it. If it does not, then don’t.‖ 線性規(guī)劃：內點法 ?Interior Point Method (Karmarkar, 1984) ? xk 0 ? 內點 November 19, 1984 內點法 與 罰函數(shù) min cTx . A x = b x = 0 Logbarrier function: min cTx ∑ log (x i) . A x = b KKT ? Newton’s Step 內點法和平面幾何 非線性優(yōu)化問題 KKT POINTS 中國古代馬鞍 ? Matlab plot: x^2 – y^2 Lagrange (17361813) ? Primal ? dual Libration of the moon 等價 與 等效 ? 在數(shù)學上等價，在計算上不一定等效 馮康（ 1920—1993) 例子： (B+ λI) d = g , || d || = Δ || d(λ) || = Δ ?? 1/ || d(λ) ||
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