IEEE Trans Cybern. 2018 Jan;48(1):277-287. doi: 10.1109/TCYB.2016.2632159. Epub 2016 Dec 28.
Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an -norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.
由于其在工程应用中的重要性，许多研究都致力于解决复变量优化问题。然而，解决复变量优化问题的复数值优化方法仍然是一个活跃的研究领域。本文分别提出了两种有效的复数值优化方法，用于求解复变量中实函数的约束非线性优化问题。一种方法解决具有线性等式约束的复数值非线性规划问题。另一种方法解决同时具有线性等式约束和范数约束的复数值非线性规划问题。从理论上讲，在较温和的条件下，我们证明了所提出的两种复数值优化算法的全局收敛性。所提出的两种算法可以完全在复域中求解复变量优化问题，并显著扩展现有的复数值优化算法。数值结果进一步表明，所提出的两种算法比几种传统的实数值优化算法具有更快的速度。
