Lectures	Date	Subjects Covered	Lecture and Supplementary Information
Lecture 35	M. Apr. 5	interior-point methods, pdf file; Ouline for final exam
		Week 13 starts
Lecture 34	W. Mar. 31	interior-point methods, pdf file;	barrier method (centering/duality gap); generalized inequalities (SOCP, SDP); maxcut.m MATLAB file
Lecture 33	M. Mar. 29	interior-point methods, pdf file; Sections in text: 11.3, 11.4	Force field interpretation; barrier method (inner centering steps); LP and GP examples; Feasibility/Phase I;
		Week 12 starts
Lecture 32	F. Mar. 26	interior-point methods, pdf file; Sections in text: 11.3	p-d i-p method for linear programming (implementation details)
Lecture 31	W. Mar. 24	interior-point methods, pdf file; Sections in text: 11.3.2	p-d i-p method for linear programming (derivation) Interpretation via perturbed KKT conditions MATLAB program for p-d i-p for LP
Lecture 30	M. Mar. 22	interior-point methods, pdf file; Sections in text: 11.2.2, 11.3.1	More on log-barrier function (gradient/Hessian) central path characterization/properties primal/dual points on central path
		Week 11 starts
Lecture 29	F. Mar. 19	interior-point methods, pdf file; Sections in text: 11.1, 11.2.1	Inequality constrained problems optimality conditions (KKT conditions) log-barrier function
Lecture 27	W. Mar. 17	Equality Constrained Minimization ( pdf file) Sections in text: 10.3.1, 10.3.2, 10.4.3	Newton step with elimination infeasible start Newton's method KKT for general equality constrained problem; and SQP methods with general equality constraints (nonconvex, not in text!!)
Lecture 26	M. Mar. 15	Equality Constrained Minimization ( pdf file) Sections in text: 10.1, 10.2	SQP approach with a merit function Newton decrement example: optimal allocation; Newton step (equivalent to solution of quadratic program) Newton decrement
		Week 10 starts
Lecture 25	F. Mar. 12	Equality Constrained Minimization ( pdf file) Sections in text: 10.	Solving KKT conditions; quadratic programming
Lecture 24	W. Mar. 10	Equality Constrained Minimization ( pdf file) Sections in text: 10.	problem 10.3 hint: use block elimination ; linear and quadratic models for steepest descent and Newton directions; affine invariance of Newton direction/step; linear equality constraints; exploit optimality conditions; quadratic program (Hessian psd on nullspace of A!!!)
Lecture 23	M. Mar. 8	Equality Constrained Minimization ( pdf file) Sections in text: 10.	review of Simple solution of Lagrangian relaxation equivalence of Boolean LP; example of nonconvergence of steepest descent due to insufficient decrease.
		Week 9 starts
Lecture 22	F. Mar. 5	Newton's method ( pdf file) Sections in text: 9.5	3 derivations (quadratic model, optimal scaling, linearization of optimality condition); affine invariance; quadratic converence
Lecture 21	W. Mar. 3	steepest descent; sections in text: 9.4 intro, 9.4.1, 9.4.2, and only a very brief mention of the material in 9.4.3 and 9.4.4.
cancelled due to injury	M. Mar. 1
		Week 8 starts
Midterm	F. Feb. 26	Lectures 1-18.	Emphasis is on homework assignments and material covered in class.
Lecture 20	W. Feb. 24	Unconstrained Minimization ( pdf file) Sections in text: 9.?	gradient descent (Cauchy's steepest descent); steepest descent on a quadratic function: steepdescquadr.m
Lecture 19	M. Feb. 22	Algorithms ( pdf file) Sections in text: 9.2	instability in solving linear equations: Aoneseps.m Minimization problem solved with a log-barrier function: barrier.m descent methods; line search; gradient descent (Cauchy's steepest descent); steepest descent on a quadratic function: steepdescquadr.m
		Week 7 starts
Lecture 18	F. Feb. 12	Algorithms ( pdf file) Sections in text: 9.1	Unconstrained Minimization: iterative methods; closed sublevel sets; strong convexity
Lecture 17	W. Feb. 10	KKT Theorem and examples	Finding the minimum eigenvalue and corresp. eigenvector (spectral theorem); finding a lower bound on the smallest eigenvalue
Lecture 16	M. Feb. 8	Duality ( pdf file) Sections in text: 5.3, 5.4, 5.5	TRS (trust region subproblem); geometric interpretation of duality; KKT conditions; Remark on TRS
		Week 6 starts
Lecture 15	F. Feb. 5	Duality	Review of Homework #2
Lecture 14	W. Feb. 3	Duality	CVX userguide, chapter 6, page 39, SDP. matlab file for SDP relaxation of random max-cut problem
Lecture 13	M. Feb. 1	Duality ( pdf file) Sections in text: 5.2	weak duality p^* ≥ d^; strong duality p^ = d^* AND d^* is ATTAINED!; constraint qualifications guarantee a zero duality gap and dual attainment;
		Week 5 starts
Lecture 12	F. Jan. 29	Duality ( pdf file) Sections in text: 5.1	Lagrangian (space where Lagrange multipliers lie); Lagrange dual function and lower bounds; Examples: linear least squares, LP, partitioning (max-cut), minimum volume covering ellipsoid.
Lecture 11	W. Jan. 27	Convex Programs ( pdf file) Sections in text: 4.6, 4.7	semidefinite programming; eigenvalue minimization; portfolio optimization (Pareto points)
Lecture 10	M. Jan. 25	Convex Programs ( pdf file) Sections in text: 4.4.2 (not minimal surfaces), 4.5.1-4.5.3	QCQP; SOCP; Robust programming Geometric Progr.
		Week 4 starts
Lecture 9	F. Jan. 22	Convex Programs ( pdf file) Sections in text: 4.4.1	(Voronoi diagrams from assignment, also for your interest only: finitely generated/polyhedral cones) quadratic programming, least squares including: bounding variance, LP with random costs, Markowitz portfolio opt. (there are many sources for info. on portfolio opt., e.g. this with conic opt.)
Lecture 8	W. Jan. 20	Convex Optimization Problems ( pdf file) Sections in text: 4.2.-4.2.4 (read 4.2.5), 4.3	( InfoSession on Grad Studies!) Set midterm date for Feb 26, 2010. download CVX (gunzip and tar xvf OR unzip/xwinzip to get the cvx directory and follow the other installation instructions) create the startupcvx.m file for the appropriate path additions. Try the cvx/matlab command quickstart. Examples of Rockafellar-Pshenichni condition Equivalent convex problems;
Lecture 7	M. Jan. 18	( perspective, conjugate functions Sections in text 3.2.6, 3.3) Convex Optimization Problems ( pdf file) Sections in text: 4.1, 4.2.2	( InfoSession on Grad Studies!) ( These old review sessions from EE364a 2009 may be useful. In particular: Review session 1 is on: examples of convex sets; affine/convex;conic hulls; preserving convexity; convex cones. Review session 2 is on: convex functions; determining convexity; preserving convex functions; conjugate functions. ) optimization problems in standard form convex optimization problems Rockafellar-Pshenichni optimality condition (nonnegative directional derivatives)
		Week 3 starts
Lecture 6	F.Jan. 15	Convex functions cont... ( pdf file) Sections in text: 3.1.6 to 3.3.2, (and read 3.5 and 3.6)	( InfoSession on Grad Studies!) further examples of characterizing convex functions; epigraph and sublevel set; Jensen's inequality; operations that preserve convexity; (read text: perspective, conjugate functions, log-convex and log-concave functions, convexity with respect to generalized inequalities)
Lecture 5	W. Jan. 13	Convex functions ( pdf file); Sections in text: 3.1.1 to 3.1.5	Examples of convex functions and matlab file for plots; Restriction to a line; Characterizations of convex functions using: gradients, and using Hessians; further examples
Lecture 4	M. Jan. 11	Dual Generalized Inequalities (pdf file)	Dual Cone Dual Generalized Inequalities (dual minimum and minimal elements) definition convex function;
		Week 2 starts
Lecture 3	F. Jan. 8	(Duality) Convex sets cont... ( pdf file)	separating (supporting) hyperplanes Generalized Inequalities (minimum and minimal elements)
Lecture 2	W. Jan. 6	Convex Sets ( pdf file)	Affine and convex sets; Convex Operations
Lecture 1	M. Jan. 4	Introduction to CO367/CM442 ( pdf file)	Structure of Class Math. Opt.; Least Squares; Nonliear Opt; Convex Opt; CVX
		Week 1 starts

Lecture Outlines and Supplementary Material, CO367/CM442 Winter'10

This webpage contains files used during the lectures. Additional material/links are also included. Be aware that this webpage is continually being polished/changed.