บทที่ 6 การหาจุดต่ำที่สุดของฟังก์ชั่นที่มีข้อจำกัด

ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME 654OPTIMUM DESIGN OFMECHANICAL PARTS

บทท�� 6 การหาจุ�ดต่ำ��าท��สุ�ดของฟั�งก�ชั่��นท��มี�

ข�อจุ�าก�ด

ด�ลยโชั่ต่ำ� ชั่ลศึ กษ์�Mechanical Engineering Department

Thammasat University

Module 6 : Constrained Optimization 2 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ห�วข�อ

6.1 ล�กษ์ณะทางเรขาคณ�ต่ำของปั�ญหา6.2 ต่ำ�วค)ณลากรานจุ� 6.3 เง*�อนไข Karush-Khun-Tucker (KKT)

Module 6 : Constrained Optimization 3 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ล�กษ์ณะทางเรขาคณ�ต่ำของปั�ญหา6.1

Module 6 : Constrained Optimization 4 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

จุ�ดท��เปั,นไปัได� – Feasible Point

• ค*อจุ�ดท��เง*�อนไขท�-งหมีดเปั,นจุร�ง• จุ�ดต่ำ��าท��สุ�ดต่ำ�องเปั,นจุ�ดท��เปั,นไปัได�

Module 6 : Constrained Optimization 5 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.างท�� 6.1

Module 6 : Constrained Optimization 6 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.างท�� 6.2

Module 6 : Constrained Optimization 7 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.างท�� 6.3

Module 6 : Constrained Optimization 8 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.างท�� 6.4

Module 6 : Constrained Optimization 9 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.างท�� 6.4 (2)

Module 6 : Constrained Optimization 10 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.างท�� 6.4 (3)

Module 6 : Constrained Optimization 11 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ข�อสุ�งเกต่ำ

Module 6 : Constrained Optimization 12 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ข�อสุ�งเกต่ำ (2)

Module 6 : Constrained Optimization 13 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วค)ณลากรานจุ�6.2

Module 6 : Constrained Optimization 14 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วค)ณลากรานจุ� (2)

Module 6 : Constrained Optimization 15 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วค)ณลากรานจุ� (2)

Lagrange multiplier

Module 6 : Constrained Optimization 16 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ฟั�งก�ชั่��นลากรานจุ�

จุ�ดต่ำ��าท��สุ�ดเก�ดข -นเมี*�อ

สุ�าหร�บปั�ญหาท��มี�ข�อจุ�าก�ดแบบเท.าก�บ

ก�าหนดให�

Module 6 : Constrained Optimization 17 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.5

Module 6 : Constrained Optimization 18 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.5 (2)

Module 6 : Constrained Optimization 19 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.5 (3)

Module 6 : Constrained Optimization 20 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

เง*�อนไข Karush-Khun-Tucker6.3การใชั่�ฟั�งก�ชั่��นลากรานจุ�ก�บปั�ญหาท��มี�ข�อจุ�าก�ดแบบไมี.เท.าก�บ

ต่ำ�องใชั่�

Module 6 : Constrained Optimization 21 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ฟั�งก�ชั่��นลากรานจุ�สุ�าหร�บปั�ญหาท��มี�ข�อจุ�าก�ดแบบไมี.เท.าก�บ

Module 6 : Constrained Optimization 22 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

เง*�อนไข KKT (1)

Module 6 : Constrained Optimization 23 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

เง*�อนไข KKT (2)

Module 6 : Constrained Optimization 24 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

Switching Conditions

m

Module 6 : Constrained Optimization 25 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.6

Module 6 : Constrained Optimization 26 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.6 (2)

Module 6 : Constrained Optimization 27 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.6 (3)

Module 6 : Constrained Optimization 28 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.6 (4)

Module 6 : Constrained Optimization 29 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.6 (5)

Module 6 : Constrained Optimization 30 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7

Module 6 : Constrained Optimization 31 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7 (2)

Module 6 : Constrained Optimization 32 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7 (3)

Module 6 : Constrained Optimization 33 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7 (4)

Module 6 : Constrained Optimization 34 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7 (5)

Module 6 : Constrained Optimization 35 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7 (6)

Module 6 : Constrained Optimization 36 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7 (7)

Module 6 : Constrained Optimization 37 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7 (8)

Module 6 : Constrained Optimization 38 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7 (9)

Module 6 : Constrained Optimization 39 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7 (10)

Module 6 : Constrained Optimization 40 ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME654

ต่ำ�วอย.าง 6.7 (11)