Two Fast Complex-Valued Algorithms for Solving Complex Quadratic Programming Problems

In this paper, we propose two fast complex-valued optimization algorithms for solving complex quadratic programming problems: 1) with linear equality constraints and 2) with both an $ {l_{1}}$ -norm constraint and linear equality constraints. By using Brandwood’s analytic theory, we prove the convergence of the two proposed algorithms under mild assumptions. The two proposed algorithms significantly generalize the existing complex-valued optimization algorithms for solving complex quadratic programming problems with an $ {l_{1}}$ -norm constraint only and unconstrained complex quadratic programming problems, respectively. Numerical simulations are presented to show that the two proposed algorithms have a faster speed than conventional real-valued optimization algorithms.