In this chapter, we will introduce two important types of convex optimization

problems, LP and QP (including quadratic constrained QP (QCQP)), which

have been widely applied in science and engineering problems. We will illustrate

them via various examples and some cutting edge applications in signal process-

ing (blind source separation in biomedical imaging and hyperspectral imaging)

and in communications (power assignment, receive beamforming, and transmit

beamforming). Through these examples and applications, the reformulation of

the original optimization into an LP or a QP is clearly illustrated through change

of variables, equivalent transformations, or representations introduced in Chap-

ter 4, though closed-formed solutions and analytical solutions, which may exist,

are usually hard to find.