This chapter presents reduced-rank linearly constrained minimum variance (LCMV) algorithms based on the concept of joint iterative optimization of parameters. The proposed reduced-rank scheme is based on a constrained robust joint iterative optimization (RJIO) of parameters according to the minimum variance criterion. The robust optimization procedure adjusts the parameters of a rank-reduction matrix, a reduced-rank beamformer and the diagonal loading in an alternating manner. LCMV expressions are developed for the design of the rank-reduction matrix and the reduced-rank beamformer. Stochastic gradient and recursive least-squares adaptive algorithms are then devised for an efficient implementation of the RJIO robust beamforming technique. Simulations for a application in the presence of uncertainties show that the RJIO scheme and algorithms outperform in convergence and tracking performances existing algorithms while requiring a comparable complexity.