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2004•Numerical Functional Analysis and OptimizationRequires access

On Second-Order Properties of the Moreau–Yosida Regularization for Constrained Nonsmooth Convex Programs

Fanwen Meng, Gongyun Zhao

Open publisher page 17 citations

Abstract

In this paper, we attempt to investigate a class of constrained nonsmooth convex optimization problems, that is, piecewise C 2 convex objectives with smooth convex inequality constraints. By using the Moreau–Yosida regularization, we convert these problems into unconstrained smooth convex programs. Then, we investigate the second-order properties of the Moreau–Yosida regularization η. By introducing the (GAIPCQ) qualification, we show that the gradient of the regularized function η is piecewise smooth, thereby, semismooth.

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What this paper is about

In this paper, we attempt to investigate a class of constrained nonsmooth convex optimization problems, that is, piecewise C 2 convex objectives with smooth convex inequality constraints. By using the Moreau–Yosida regularization, we convert these problems into unconstrained smooth convex programs. Then, we investigate the second-order properties of the Moreau–Yosida regularization η. By introducing the (GAIPCQ) qualification, we show that the gradient of the regularized function η is piecewise smooth, thereby, semismooth.

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OpenAlex reports 17 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we attempt to investigate a class of constrained nonsmooth convex optimization problems, that is, piecewise C 2 convex objectives with smooth convex inequality constraints. By using the Moreau–Yosida regularization, we convert these problems into unconstrained smooth convex programs. Then, we investigate the second-order properties of the Moreau–Yosida regularization η. By introducing the (GAIPCQ) qualification, we show that the gradient of the regularized function η is piecewise smooth, thereby, semismooth.

Key concepts: Mathematics, Proximal gradient methods for learning, Piecewise, Subderivative, Regularization (linguistics), Convex function, Regular polygon, Proper convex function

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