Lecture II (Days 5,6,7,8): Applications/Algorithms

1. Applications

   1. (Robust) Approximation Notes, 6.18; (Robust) Approximation Slides; (Robust) Approximation Book pages;

      Stochastic robust approx., worst-case robust approx., uncertainty sets

   2. Geometric Problems Notes, 8...; Geometric Problems Slides; Geometric Problems Book pages;

      Minimum (maximum) volume ellipsoids, analytic center, linear discrimination, robust linear discrimination, support vector classifier sets

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2. Algorithms

   9. Unconstrained Minimization Notes, 9; Unconstrained Minimization Slides; Unconstrained Minimization Book pages;

      strong convexity, descent methods, line searches, steepest descent, Newton's method, implementation, nondescent methods
      MATLAB optimization examples: files objfun1.m, rununc1.m

   10. Equality constrained Minimization Notes, 9; Equality constrained Minimization Slides; Equality constrained Minimization Book pages;

       QPs, eliminations, Newton step, solving KKT system

   11. Interior-point Methods Notes, 9; Interior-point Methods Slides; Interior-point Methods Book pages;

       log-barrier, central path, KKT optimality conditions, SDP and SOC
       SQP Methods; Sequential Quadratic Programming and Filter Methods; SQ²P, Sequential Quadratic Constrained Quadratic Programming; Reduced-Gradient Methods; More Methods for General NLP....
       MATLAB optimization examples: files objfun2.m, confun2.m, runconstr2.m; objfungrad3.m, confungrad3.m, runconstr3.m; findzero.m;

Supplementary Information

• NEOS Server Stories

• Suggested Texts/References:

  • Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications

    by Aharon Ben-Tal and Arkadi Nemirovski
    MPS/SIAM Series on Optimization 2
    URL: http://www.ec-securehost.com/SIAM/MP02.html

  • Numerical Optimization

    Jorge Nocedal Stephen J. Wright
    URL: http://www.ece.northwestern.edu/~nocedal/book/num-opt.html
  • Lecture Notes for/from Boyd and Vandenberghe book

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Users' Home Pages on orion.math,

Supplementary Information

• NEOS Server Stories

• Suggested Texts/References:

  • Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications

    by Aharon Ben-Tal and Arkadi Nemirovski
    MPS/SIAM Series on Optimization 2
    URL: http://www.ec-securehost.com/SIAM/MP02.html

  • Numerical Optimization

    Jorge Nocedal Stephen J. Wright
    URL: http://www.ece.northwestern.edu/~nocedal/book/num-opt.html
  • Lecture Notes for/from Boyd and Vandenberghe book

Start of 's Home Page (more ambigrams)
Users' Home Pages on orion.math,