MAI391_-_Pactice_-_Questions_191.webp

Find the dual Lagrangian \mathfrak{D}(\lambda) of the following quadratic programming
min x_{1}^{2}+3x_{2}^{2} subject to x_{1}+x_{2}\le1 2x_{1}-x_{2}\le-2
(i) -\frac{1}{3}\lambda_{1}^{2}-\frac{5}{6}\lambda_{1}\lambda_{2}-\frac{13}{12}\lambda_{2}^{2}+\lambda_{1}-2\lambda_{2}
(ii) -\frac{1}{3}\lambda_{1}^{2}+\frac{5}{6}\lambda_{1}\lambda_{2}-\frac{13}{12}\lambda_{2}^{2}-\lambda_{1}+2\lambda_{2}
(iii) -\frac{1}{3}\lambda_{1}^{2}-\frac{5}{6}\lambda_{1}\lambda_{2}+\frac{13}{12}\lambda_{2}^{2}+\lambda_{1}-2\lambda_{2}
(iv) -\frac{1}{3}\lambda_{1}^{2}-\frac{5}{6}\lambda_{1}\lambda_{2}-\frac{13}{12}\lambda_{2}^{2}-\lambda_{1}+2\lambda_{2}