15. Barrier Method

이 장에서는 2nd-order method 중 하나인 Barrier Method에 대해 살펴보도록 하겠다.

Barrier Method는 2nd-order method 문제 중에 가장 어려운 문제라고 할 수 있는 Inequality constraint와 equality constrained smooth problem을 풀기 위한 방법이다.

(참고로, 최적화 문제를 풀 때 gradient를 사용하면 1st-order method라고 하며 hessian을 사용하면 2nd-order method라고 한다.)

References and further readings

• S. Boyd and L. Vandenberghe (2004), “Convex optimization”, Chapter 11
• A. Nemirovski (2004), “Interior-point polynomial time methods in convex programming”, Chapter 4
• J. Nocedal and S. Wright (2006), “Numerical optimization”, Chapters 14 and 19

• 15-01 Barrier method and log barrier function
• 15-01-01 Inequality constrained minimization problems
• 15-01-02 Log barrier function & barrier method
• 15-01-03 Log barrier calculus
• 15-02 Central path
• 15-03 Properties and interpretation
• 15-03-01 Perturbed KKT conditions
• 15-03-02 Suboptimality gap
• 15-04 Barrier method v.0 and v.1
• 15-05 Convergence analysis
• 15-06 Barrier method v.2
• 15-07 Feasibility methods
• 15-08 Formal barrier method