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Wrong term in formulas 7.51 & 7.52 #731

Open jqhoogland opened 1 year ago

jqhoogland commented 1 year ago

Describe the mistake The formulas for the dual optimization problem to a quadratic program contain an incorrect extra $\mathbf{A}$.

Location 6th printing; Chapter 7; Page 216; Equations 7.51 & 7.52

Proposed solution

Instead of (7.51): $$\mathcal{D}(\boldsymbol{\lambda}) = -\frac{1}{2}(\mathbf{c}+\mathbf{A}^T\mathbf{\lambda})^T\mathbf{A}\mathbf{Q}^{-1}(\mathbf{c}+\mathbf{A}^T\mathbf{\lambda})-\mathbf{\lambda}^T\mathbf{b}$$

It should be: $$\mathcal{D}(\boldsymbol{\lambda}) = -\frac{1}{2}(\mathbf{c}+\mathbf{A}^T\mathbf{\lambda})^T\mathbf{Q}^{-1}(\mathbf{c}+\mathbf{A}^T\mathbf{\lambda})-\mathbf{\lambda}^T\mathbf{b}$$

Likewise for 7.52.