Two Fast Complex-Valued Algorithms for Solving Complex Quadratic Programming Problems
提出了两种快速复值优化算法，分别用于求解带线性等式约束和同时带L1范数约束与线性等式约束的复二次规划问题，并证明了收敛性，数值模拟显示比传统实值算法更快。
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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -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.