Advanced Optimization Methods/Conical Optimization

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Department of Computer Science

Synopsis:

Motivating examples. Conic optimization: Convex cones, Primal and dual conic problems, Spectrahedra and LMIs, Spectrahedral shadows, SDP duality, Numerical SDP solvers, Exact SDP solvers. Finite-dimensional polynomial optimization: Measures and moments, Riesz functional, moment and localizing matrices, Lasserres hierarchy, Global optimum recovery, Software interfaces, Back to the motivating examples. Infinite-dimensional polynomial optimization. Extensions to time-varying coefficients. The motivating examples revisited.

Requirements:

Syllabus of lectures:

1.Motivating examples. Algebraic modelling languages.

2.Conic optimization: Convex cones, Primal and dual conic problems, Spectrahedra and LMIs, Spectrahedral shadows.

3.SDP duality, Numerical SDP solvers.

4.Exact SDP solvers and associated algebraic geometry.

5.Finite-dimensional polynomial optimization: an overview.

6.Measures and moments, Riesz functional.

7.Commutative POP: moment and localizing matrices, Lasserres hierarchy.

8.Non-commutative POP: moment and localizing matrices, NPA hierarchy.

9.Global optimum recovery.

10.Infinite-dimensional polynomial optimization.

11.Optimal control.

12.Extensions to time-varying coefficients.

13.The motivating examples revisited.

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No time-table has been prepared for this course

The course is a part of the following study plans: