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Automatic dualization

Outline. YALMIP?Recent developmentsAutomatic dualizationPrimal-dual conic problemsWhat is the problem?ImplementationApplications of automatic dualizationConclusions. What is YALMIP?. Free MATLAB toolbox for rapid definition, manipulation and solution of optimization problems.Originally a

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Automatic dualization

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    1. Automatic dualization Johan Löfberg

    2. Outline YALMIP? Recent developments Automatic dualization Primal-dual conic problems What is the problem? Implementation Applications of automatic dualization Conclusions

    3. What is YALMIP?

    4. Supported solvers

    5. Recent developments 1. Strengthened modelling framework for non-convex problems

    7. Primal-dual conic pairs Everything revolves around the primal-dual conic pair

    8. Primal-dual conic pairs Much more convenient in practice to allow free variables (equality constraints)

    9. Primal or dual? Example: Silly LP

    10. Primal or dual? Example: MAXCUT

    11. Problem: Data (C,A,b,F,f) not unique (including dimensions) Primal or dual?

    13. Where are we?

    14. Input: Symbolic YALMIP model (with constraints ) Implementation

    15. Implementation First step: Find simple primal cones

    16. Implementation Second step : Find translated primal cones

    17. Implementation Third step: Introduce slacks for dual cones

    18. Implementation

    20. MAXCUT

    21. Sum-of-squares

    22. Sum-of-squares

    23. Sum-of-squares

    24. Stability analysis

    25. Outlook & conclusion Automatic decision to dualize? Dualize quadratic objective functions? Partial dualization? Performance for large-scale problems... Very simple but very useful Commands:

    26. Download

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