TMA 4180 Optimization Theory

Lecture Plan/Actual material, spring term 2010

Actually lectured material listed in red.

Date	Topics Planned/actual	N&W Notes	Comments
Week 2 2^nd lecture	Informal summary about the course Feasible set Taylor Formula	See web page and Wikipedia Se N&W and notes
Week 3 1^st lecture	Directional derivative 1^st and 2^nd order necessary and sufficient conditions Differentiable functions Convex set and functions	Se N&W and notes
2^nd lecture	Differentiable convex functions Main theorem for convex optimization Line-search and Trust region philosophies The Test Problem Brief discussion about Newton	Covered in the note and N&W, Ch. 2
Week 4 1^st lecture	Basic Line Search theory Steepest Descent Num. experiments Steepest Descent Convergence	N&W Chapter 3 Basic Note	Banana Function and Steepest Descent Steepest Descent Demo
2^nd lecture	One-dimensional minimization. The Amoeba algorithm Numerical experiments using Matlab Trust Region Methods	See Note N&W Chapter 4	Only covered in the note Amoeba Presentation Numerical Experiments
Week 5 1^st lecture	Algorithm, sol. of the quadratic problem. Basic Hilbert space theory Conjugate gradient method (CG)	Note on main page Covered in Basic Note N&W Chapter 5
2^nd lecture	CG – final derivation CG – Convergence and num. experiments CG –Preconditioning CG – general problems	CG note CG note, N&W, 112-8 N&W, 118-20 N&W, Sec. 5.2	(see main page) CG presentation
Week6 1^st lecture	Least Square Problems	N&W Chapter 10 Extra note	(Note on main page)
2^nd lecture	Quasi-Newton. The SR1 method Nonlinear Least Squares Matlab Optimization Toolbox	N&W Ch. 6.2 N&W Chapter 10 (see main page)
Week 7 1^st lecture	Constrained optimisation (CO)	N&W Chapter 12
2^nd lecture	Karush-Kuhn-Tucker (KKT) Theorem	N&W Chapter 12	See note about KKT on the main page.
Week 8 1^st lecture	KKT and Convexity Second Order Conditions	N&W Chapter 12
2^nd lecture	Second Order Conditions, cont. Introduction to Linear programming (LP)		See note about LP on the main page
Week 9 1^st lecture	Duality
2^nd lecture	MID-TERM TEST, MARCH 4, 10:15-12:00
Week 10 1^st lecture	LP continued, Simplex method
2^nd lecture	Simplex method, continued Optimal network flow example		All slides: See main page.
Week 11 1^st lecture	Quadratic Programming Active Set Methods
2^nd lecture	Gradient Projection Methods Wolfe’s dual problem
Week 12 1^st lecture	Penalty and Barrier Methods Interior methods for LP		See Penalty and Barrier note on the main page.
2^nd lecture	Interior methods, cont. Inverse Problems
Week 13	Easter
Week 14 1^st lecture	Easter
2^nd lecture	Introduction to Variational calculus Gâteaux derivative Computing derivatives		Note about interchanging the derivative and integral on main page
Week 15 1^st lecture	Convexity The standard functional Partial Convexity
2^nd lecture	First Main Theorem Second Main theorem Free boundary problems Brachistochrone		Brachistochrone pres. on main page
Week 16 1^st lecture	Optimal production strategy Problems with constraints		Opt. Production Opt. Fuel Consumption
2^nd lecture	Theorem 3.16, Hanging Cable. PDEs and Variational Calculus		Var. Calculus and PDEs
Week 17 1^st lecture	Variational Calculus and Sport Optimal exam preparation		Var. Calculus And Sport Opt. Exam Preparation
2^nd lecture	No lecture
MAY 21	Exam 4 hours, Examination aids: C