Convex Duality in Constrained Portfolio Optimization

Convex Duality in Constrained Portfolio Optimization

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Convex Duality in Constrained Mean-variance 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...

A Robust Knapsack Based Constrained Portfolio Optimization

Many portfolio optimization problems deal with allocation of assets which carry a relatively high market price. Therefore, it is necessary to determine the integer value of assets when we deal with portfolio optimization. In addition, one of the main concerns with most portfolio optimization is associated with the type of constraints considered in different models. In many cases, the resulted p...

Convex Optimization and Lagrangian Duality

Finally the Lagranage dual function is given by g(~λ, ~ν) = inf~x L(~x,~λ, ~ν) We now make a couple of simple observations. Observation. When L(·, ~λ, ~ν) is unbounded from below then the dual takes the value −∞. Observation. g(~λ, ~ν) is concave1 as it is the infimum of a set of affine2 functions. If x is feasible solution of program (10.2)(10.4), then we have the following L(x,~λ, ~ν) = f0(x)...