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課程名稱 |
非線性最佳化之理論與應用
Nonlinear Optimization: Theory and Applications |
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開課學期 |
110-1 |
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授課對象 |
電機資訊學院 資料科學碩士學位學程 |
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授課教師 |
李育杰 |
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課號 |
Data5005 |
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課程識別碼 |
946 U0050 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期四2,3,4(9:10~12:10) |
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上課地點 |
共402 |
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備註 |
限碩士班以上 或 限博士班
總人數上限：30人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
第一週 數學預備知識
第二週 最小平方法 (我機器學習的第一課)
第三週 Nonlinear programming concept and preliminary
第四週 Linear inequality and theorems of alternative
第五週 Theorems of alternative and separation theorem
第六週 Convex sets, convex and concave functions
第七週 Saddle point optimality conditions without differentiability
第八週 Saddle point optimality conditions without differentiability
第九週 期中考週
第十週 Saddle point optimality conditions with differentiability
第十一週 Saddle point optimality conditions with differentiability
第十二週 Duality in nonlinear programming
第十三週 Duality in nonlinear programming
第十四週 Optimality and duality in generalized convex and concave functions
第十五週 Nonlinear programming in machine learning
第十六週 Nonlinear programming in machine learning
第十七週 Review
第十八週 期末考週 |
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課程目標 |
Numerical optimization has become the most important key element of the modern machine learning. This course, Nonlinear Programming, provides the theoretical foundation for the numerical optimization. We start with the linear inequalities and theorems of the alternative that will be the very useful tools for deriving the optimality criteria of constrained optimization problems. We include the duality in nonlinear programming as well as necessary and sufficient optimality conditions of nonlinear programming. |
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課程要求 |
Calculus
Mathematical analysis
Numerical Methods
Linear Algebra
Probability
Homework: 40%
Midterm Exam: 30%
Final Exam: 30% |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
Olvi L. Mangasarian (1994), Nonlinear Programming (Classics In Applied Mathematics), ISBN: 0-89871-341-2 |
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評量方式
(僅供參考) |
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