Summary: Examination: Mathematical Programming I (158025)
June 30, 2003, 13.30-16.30
Ex.1 Prove the following statements.
(a) Let A Rn×m
be a given matrix (m n). Then AT
A is positive definite if
and only if A has full rank .m/.
(b) For a symmetric .n×n/-matrix A the following holds: A is positive semidef-
inite if and only if all eigenvalues j of A are non-negative (j 0; j =
1;:::;n).
Ex.2 Consider the primal-dual pair of linear problems:
.P/ max
xRn
cT
x s.t. Ax b
.D/ min
yRm
bT
y s.t. AT
y = c ; y 0

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

Collections: Engineering