# Constrained Optimization Involving Nonconvex 𝓁p Norms: Optimality Conditions, Algorithm and Convergence

@article{Wang2021ConstrainedOI, title={Constrained Optimization Involving Nonconvex 𝓁p Norms: Optimality Conditions, Algorithm and Convergence}, author={Hao Wang and Yining Gao and Jiashan Wang and Hongying Liu}, journal={ArXiv}, year={2021}, volume={abs/2110.14127} }

This paper investigates the optimality conditions for characterizing the local minimizers of the constrained optimization problems involving an `p norm (0 < p < 1) of the variables, which may appear in either the objective or the constraint. This kind of problems have strong applicability to a wide range of areas since usually the `p norm can promote sparse solutions. However, the nonsmooth and non-Lipschtiz nature of the `p norm often cause these problems difficult to analyze and solve. We…

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