Reconfigurable intelligent surface (RIS)-aided networks have been investigated for the purpose of improving the system performance. However, the introduced unit modulus phase shifts and coupling characteristic bring enormous challenges to the optimization in the RIS-aided networks. Many efforts have been made to jointly optimize phase shift vector and other parameters. This article intends to survey the latest research results about the optimization in RIS-aided networks. A taxonomy is devised to categorize the existing literatures based on optimization types, phase shift form, and decoupling methods. Furthermore, in alternating optimization framework, we introduce in detail how to exploit the aforementioned technologies flexibly. It is known that most works could not guarantee a stationary point. To overcome this problem, we propose a unified framework for the optimization problem of RIS-aided networks with continuous phase shifts to find a stationary point. Finally, key challenges are outlined to provide guidelines for the domain researchers and designers to explore more efficient optimization frameworks, and then open issues are discussed.
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