MATH 4420 Final: Math4420 Final Exam
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Problem 1 (a) consider the problem of minimizing a general quadratic function subject to a linear constraint: min. 2 xt qx ct x subject to ax = b where q = qt > 0, a rm n, m < n, rank a =m. Derive a closed-form solution to the problem. (b) the shortest distance from the origin to the line in 3d is computed by minimizing min. 3) subject to x1 + x2 x3 = 3 x1 x2 + 2x3 = 1. Solve this optimization problem, either directly or using part (a). State the necessary and su cient condition of optimality (1st order and 2nd order). Solve the following linear programming problem using the simplex tableau method max. 3x1 + 2x2 subject to x1 4, x2 1.
