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In this paper, we develop a systematic design optimization methodology for inductively degenerated cascode CMOS low noise amplifiers (LNA) in fully integrated wideband and multi-band wireless systems. Leveraging an accurate analytical circuit model, we combine global and local numerical optimization techniques in a hierarchical manner to simultaneously determine the fixed and switchable passive component and device parameters in the LNA circuit necessary to meet user-specified performance requirements. To demonstrate the effectiveness of proposed design optimization methodology, we utilize the method to create 3 wideband and 3 multi-band LNA designs that meet a wide-range of impedance matching, noise figure, gain, power dissipation, and linearity requirements. The proposed method provides circuit designers with a fast and effective means for the rapid prototyping and design space exploration of wideband and multi-band inductively degenerated cascode CMOS LNAs.