  This paper proposes two algorithms to maximize the minimum array power gain
in a wide-beam mainlobe by solving the power gain pattern synthesis (PGPS)
problem with and without sidelobe constraints. Firstly, the nonconvex PGPS
problem is transformed into a nonconvex linear inequality optimization problem
and then converted to an augmented Lagrangian problem by introducing auxiliary
variables via the Alternating Direction Method of Multipliers (ADMM) framework.
Next,the original intractable problem is converted into a series of nonconvex
and convex subproblems. The nonconvex subproblems are solved by dividing their
solution space into a finite set of smaller ones, in which the solution would
be obtained pseudoanalytically. In such a way, the proposed algorithms are
superior to the existing PGPS-based ones as their convergence can be
theoretically guaranteed with a lower computational burden. Numerical examples
with both isotropic element pattern (IEP) and active element pattern (AEP)
arrays are simulated to show the effectiveness and superiority of the proposed
algorithms by comparing with the related existing algorithms.
