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A stochastic primal-dual method for a class of nonconvex constrained optimization

Lingzi Jin () and Xiao Wang ()
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Lingzi Jin: University of Chinese Academy of Sciences
Xiao Wang: University of Chinese Academy of Sciences

Computational Optimization and Applications, 2022, vol. 83, issue 1, No 5, 143-180

Abstract: Abstract In this paper we study a class of nonconvex optimization which involves uncertainty in the objective and a large number of nonconvex functional constraints. Challenges often arise when solving this type of problems due to the nonconvexity of the feasible set and the high cost of calculating function value and gradient of all constraints simultaneously. To handle these issues, we propose a stochastic primal-dual method in this paper. At each iteration, a proximal subproblem based on a stochastic approximation to an augmented Lagrangian function is solved to update the primal variable, which is then used to update dual variables. We explore theoretical properties of the proposed algorithm and establish its iteration and sample complexities to find an $$\epsilon$$ ϵ -stationary point of the original problem. Numerical tests on a weighted maximin dispersion problem and a nonconvex quadratically constrained optimization problem demonstrate the promising performance of the proposed algorithm.

Keywords: Nonconvex optimization; Augmented Lagrangian function; Stochastic gradient; $$\epsilon$$ ϵ -stationary point; Complexity; 90C30; 90C06; 65K05; 92C15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-022-00384-w

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