FE501 – Reading OMF2 - Nonlinear

FE501 – Reading OMF2 - NonlinearCH5 Quadratic Programming: Theory and AlgorithmsExample 5.1 (Asset Allocation)Sensitivity AnalysisRidge and Lasso RegressionCH20 Nonlinear Programming: Theory and AlgorighmsNonlinear ProgrammingOptimality conditionsUnconstrained CaseConstrained caseConvexity

CH5 Quadratic Programming: Theory and Algorithms

A quadratic program can be written in the generic form:

\begin{matrix} (1) & \begin{matrix} min_{x} \frac{1}{2} x^{T} Q x + c^{T} x \\ s . t . A x = b \\ D x \geq d \end{matrix} \end{matrix}

Example 5.1 (Asset Allocation)

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\begin{aligned} v a r (c_{1} X_{1} + c_{2} X_{2} + . . . + c_{n} X_{n}) = \\ [c_{1}, c_{2}, . . . c_{n}] (coveriance matrix) [c_{1}, c_{2}, . . . . . c_{n}]^{T} \end{aligned}

Formula for coveriance matrix is:

\begin{matrix} (2) & [\begin{matrix} V a r (x_{1}) & . . . & C o v (x_{1}, x_{n}) \\ : & . & : \\ : & . & : \\ C o v (x_{n}, x_{1}) & . . . & V a r (x_{n}) \end{matrix}] \end{matrix}

Here, the problem given the correlation matrix, and we need to calculate the covveriance matrix first:

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Sensitivity Analysis

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Ridge and Lasso Regression

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CH20 Nonlinear Programming: Theory and Algorighms

Nonlinear Programming

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Optimality conditions

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Unconstrained Case

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Constrained case

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Convexity

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