Convex Optimization

and Engineering Applications - 01OUWOQ

 
 
 


Convex Optimization and Engineering Applications - 01OUWOQ


  1. -Introduction. Functions, hyperplanes, halfspaces, etc.

  2. -Basic optimization problems: Projection theorems

  3. -Systems of linear equations, Least Squares (LS)

  4. -SVD-based optimization

  5. -Convexity. Optimization problems in standard form, optimality criteria

  6. -Linear Programming (LP), Ell-one norm optimization, Chebychev approximation

-Application examples: generation of force/torque via thrusters, uniform illumination of patch surfaces, etc.

- Quadratic Programming (QP) and Second Order Cone Programming (SOCP)

- Application examples:  FIR filter design, antenna array design, sidelobe level minimization in beamforming

- Linear Matrix Inequalities (LMI) and semidefinite programming (SDP)

- Introduction to software tools CVX and/or YALMIP

- Applications: data-fitting, approximation and estimation, truss-structural design, transistor sizing, uncertain and robust Least Squares, Bounded-Real Lemma, passivity and applications in circuit theory

- Geometrical problems: containment of poyhedra, classification, Lowner-John ellipsoids, linear discrimination, support vector machines

- Introduction to solution algorithms

- Focus seminar (tentatively)


Instructor:

Prof. Giuseppe Carlo Calafiore (giuseppe.calafiore@polito.it)

Tel.: +39-011-0907071

 
This is an interdisciplinary course that concentrates on recognizing convex optimization problems that arise in various branches of engineering, and provides the basic knowledge on how to solve them. Convex sets, functions, and optimization problems. Basics of convex analysis. Linear equations, Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering. Prerequisites: Good knowledge of linear algebra, geometry, analysis and exposure to probability. Exposure to numerical computing, optimization, systems and control theory, and application fields is helpful but not strictly required.

Program

 


Some of the material treated in the course is available in a new textbook, which is still in preparation:

- L. El Ghaoui and G. Calafiore, Optimization Models, Cambridge University Press, in preparation. Students can find a preliminary draft of the textbook in our shared Dropbox folder.


An excellent (although “advanced”) reference book is also the following classical one:

  1. -S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press,

http://www.stanford.edu/~boyd/cvxbook/

Reference Textbooks