Work

New Bounds for Exact Penalized Cardinality-Constrained Optimization with Pseudonormality Conditions

Year: 2026

Type: preprint

Abstract: Cardinality-constrained optimization (CCO) is a popular topic in sparse learning and signal recovery, yet remains challenging due to the inherent nonconvexity and discontinuity of cardinality constraints. This paper investigates the exact penalty theory for CCO problems with general equality and inequality constraints. In particular, we extend the pseudonormality condition to the cardinality-constrained framework and establish the local exact penalization without imposing Lipschitz continuity on the objective function. We further analyze both the projected subgradient method and its stochastic variant with convergence guarantees for the derived exact penalty formulation. Compared with the existing results, we give some more precise bounds of the iterate sequence and the objective function value.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2605.16687

Authors: Pan, Lili, Xie, Huilin, Xiu, Xianchao, Tao, Jiyuan

Institutions: Shandong University of Technology, Shanghai University, Loyola University Maryland

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G1700846800, G5300160718

OpenAlex ID: W7161704340

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