Relaxation approximation of Friedrichs' systems under convex constraints

Relaxation approximation of Friedrichs' systems under convex constraints

Best Approximation under a Convex Paranorm

We introduce the q-paranorm, investigate some of its properties. We further give an algorithm which constructs the best linear approximations under the q-paranorm.

Convex duality in mean-variance hedging under convex trading constraints

We study mean-variance hedging under portfolio constraints in a general semimartingale model. The constraints are formulated via predictable correspondences, meaning that the trading strategy is restricted to lie in a closed convex set which may depend on the state and time in a predictable way. To obtain the existence of a solution, we first establish the closedness in L2 of the space of all g...

Structured Convex Optimization under Submodular Constraints

A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and we show that a wide range of convex optimization problems under submodular constraints can be solved much more efficiently than general submodular optimizatio...

On utility maximization under convex portfolio constraints