General information 
Course unit name: Optimization
Course unit code: 572662
Academic year: 20192020
Coordinator: Gerardo Gomez Muntane
Department: Department of Mathematics and Computer Science
Credits: 6
Single program: S
Estimated learning time 
Total number of hours 150 
Facetoface learning activities 
60 
 Lecture 
30 

 Problemsolving class 
30 
Supervised project 
45 
Independent learning 
45 
Competences to be gained during study 
That the students acquire knowledge and understanding that provide them a basis or opportunity for originality in developing and / or applying ideas, often in a research context

Learning objectives 
Referring to knowledge That the students can apply their knowledge and their ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their field of study 
Teaching blocks 
1. I. Unconstrained optimization and optimality conditions
* I.1 Nonlinear programming
I.2 Application contexts
I.3 Characterization issue
I.4 Computation issue
I.5 Duality
I.6 Unconstrained optimization
I.7 Local minima
I.8 Necessary conditions
I.9 Sucient conditions for local minima
I.10 The role of convexity
2. II. Gradient methods for unconstrained optimization
* II.1 Quadratic unconstrained problems
II.2 Existence of optimal solutions
II.3 Iterative computational rethods
II.4 Gradient methods. Motivation
II.5 Principal gradient methods
II.6 Choices of direction and stepsize
II.7 Convergence
3.
III. Newton and GaussNewton methods
* III.1 Newtons method
III.2 Convergence
III.3 Variants of Newtons method
III.4 Least squares problems
III.5 The GaussNewton method
III.6QuasiNewton methods
4. IV. Convexity
* IV.1 Convex sets and convex functions
IV.2 Diㄦential properties of convex functions
IV.3 Extrema of convex functions
IV.4 Optimality conditions for convex programms
IV.5 Optimization subect to bounds
IV.6 Optimization over a simplex
IV.7 Optimal routing
IV.8 Projection over a convex set
5. V. Constrained optimization. Lagrange multipliers
* V.1 Equality constrained problems
V.1.1 Lagrange multiplier theorem
V.1.2 Equality constrained problems. Sucientciency conditions
V.1.3 Convexi^Lcation using augmented Lagrangians
V.1.4 Sensitivity
V.2 Inequality Constrained Problems
V.2.1 Necessary and subectcient conditions
V.2.2 Linear constraints
6. VI. Duality
* VI.1 Convex cost. Linear constraints
VI.2 Duality theorem
VI.3 Linear programming duality
VI.4 Quadratic programming duality
VI.5 Geometrical framework for duality
VI.6 Geometric multipliers
VI.7 The dual problem
VI.8 Properties of the dual function
VI.9 Duality and Gmultipliers
VI.10 Strong duality theorem
VI.11 Linear equality constraints
7. VII. Interior point methods
* VII.1 Barrier and interior point methods
VII.2 Linear programs and the logarithmic barrier
VII.3 Path following using Newtons method
8.
VIII. Penalty methods
* VIII.1 Quadratic penalty methods
VIII.2 Multiplier methods
9. IX. Stochastic Optimization
Teaching methods and general organization 
Presentation, by the teacher, of the main ideas and results of the different thematic blocks,and resolution, by the students, of exercises 
Official assessment of learning outcomes 
 Resolution of exercises (50% of the final mark)
Examinationbased assessment  Final exam 
Reading and study resources 
Consulteu la disponibilitat a CERCABIB
Book
Avriel, M. Nonlinear programming : analysis and methods. Mineola, NY : Dover Publications, 2003.
Bertsekas, Dimitri P. Nonlinear programming. Belmont, Mass. : Athena Scientific, [2016].
Boyd, S. ; Vandenberghe, L. Convex optimization. Cambridge : Cambridge University Press, 2004.