### Erling Andersen (MOSEK ApS, Denmark)

#### From linear to conic optimization

*Wednesday 18 March 2009 at 15.30, JCMB 6206*

##### Abstract

Linear optimization (aka LP) is a highly successful operations
research model. Therefore, it is natural to generalize the linear
optimization model to handle general nonlinear relationships.
However, this give rise to many difficulties such as lack of
efficient algorithms and software, lack of duality, problems with
global versus local optimums just to mention a few.

In the recent years a new class of optimization models known as
conic optimization problems has appeared which deals with the
problem of minimizing a linear function subject to an affine set
intersected with a convex cone. Although the conic optimization
model seems restricted then any convex optimization model can be
cast as a conic optimization model. Moreover, the conic optimization
model has many interesting applications in image processing,
finance, economics, combinatorial optimization etc.

The purpose of this talk is to present the conic optimization
model and to demonstrate it allows the formulation and solution of
certain nonlinear optimization models as easy as if they were an
linear optimization problem. In particular we review several
interesting applications of conic optimization. We also present
the main ideas behind the efficient interior-point based solution
algorithms for conic optimization.

The talk should be interesting for any user of linear optimization
and only requires basic knowledge about linear optimization.

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