Portfolio Optimization

86 Quadratic Programming Geometry Chap. 5

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Figure 5.3 Geometry of Example 5.3.

5.2 Geometry of QP Optimality

Conditio ns

An optimal solution for a linear programming pro blem is charac-

terized by the condition that the negative gr adient o f the objective

function lies in the cone spanned by the gradients of those constraints

active at it. Under a simple assumption, the same characterization holds

for a quadratic programming problem. Recalling that the gradient of

a function is j ust t he vector of first partial derivatives, t he gradient of

Sec. 5.2