This course will be an introduction to mathematical programming with an emphasis on basic theories for nonlinear programming and efficient techniques for the solution of combinatorial optimization. The first part of the course will be given by me, and the second part by prof. Shurbevski. For the second part, see here.

Contents and materials:

English-Japanese dictionary of terms used in the class [pdf]

Class 1: Introduction, notations, convexity, cones, first-order optimality conditions [pdf]

Class 2: Farkas’ lemma and Carathéodory’s theorem [pdf]

Class 3: KKT conditions and constraint qualifications [pdf]

※ Report no. 1 [pdf]

Class 4: Dual problems and weak duality theorem [pdf]

Class 5: Separation theorems and strong duality [pdf]

※ Report no. 2 [pdf]

Class 6: Applications of duality theory [pdf]

Class 7: More results using duality theory [pdf]

※ Final Report [pdf]

→ Check your grade at PandA. (updated)

Some other references:

• D. P. Bertsekas, "Nonlinear Programming", Athena Scientific, 3rd edition, 2016.
• 福島雅夫，「非線形最適化の基礎」，朝倉書店，2001.
• 山下信雄，「非線形計画法」（応用最適化シリーズ6），朝倉書店，2015.