HfO₂ based ferroelectric FET (FeFET) has recently received great interest for its application in nonvolatile memory (NVM) [1]. Unlike conventional perovskite based ferroelectric materials, HfO₂ is CMOS compatible and retains ferroelectricity for thin film with thickness around 10 nm. Therefore, successful integration of ferroelectric HfO₂ into advanced CMOS technology makes this technology highly promising for NVM [1]. Moreover, by tuning the portion of switched ferroelectric domain, a FeFET can exhibit multiple intermediate states, which enables its application as an analog conductance in mixed-signal in-memory computing. Currently, such architectures have been applied to neuromorphic computing [2], [3]. In this paper, we present a processing-in-memory (PIM) architecture with FeFETs and demonstrate how this can be used to solve a new class of optimization problems, in particular, distributed least square minimization.