Convex Duality in Constrained Portfolio Optimization

Discrete-Time Constrained Portfolio Optimization: Strong Duality Analysis

We study in this paper the strong duality for discrete-time convex constrained portfolio selection problems when adopting a risk neutral computational approach. In contrast to the continuous-time models, there is no known result of the existence conditions in discrete-time models to ensure the strong duality. Investigating the relationship among the primal problem, the Lagrangian dual and the P...

Convex Duality in Constrained Mean-variance Portfolio Optimization

Convex risk measures for portfolio optimization and concepts of flexibility

Due to their axiomatic foundation and their favorable computational properties convex risk measures are becoming a powerful tool in financial risk management. In this paper we will review the fundamental structural concepts of convex risk measures within the framework of convex analysis. Then we will exploit it for deriving strong duality relations in a generic portfolio optimization context. I...

On the duality of quadratic minimization problems using pseudo inverses

‎In this paper we consider the minimization of a positive semidefinite quadratic form‎, ‎having a singular corresponding matrix $H$‎. ‎We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method‎. ‎Given this approach and based on t...

SOME PROPERTIES FOR FUZZY CHANCE CONSTRAINED PROGRAMMING

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

Ee 381v: Large Scale Optimization 12.1 Last Time 12.2 Quadratically Constrained Quadratic Program

In the previous lecture, in the first place, we talked about duality for general non-convex optimization. And we know that dual functions are always convex. The dual of the dual problem is also convex. In applications, the dual of the dual can be used as the convex relaxation of the primal (and we will see this explicitly in the next lecture). Then, we covered the concepts of weak duality and s...