Erling D. Andersen
From linear to conic optimization
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.