Generalized damped Newton algorithms in nonsmooth optimization via second-order subdifferentials

Pham Duy Khanh (), Boris S. Mordukhovich (), Vo Thanh Phat () and Dat Ba Tran ()
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Pham Duy Khanh: HCMC University of Education
Boris S. Mordukhovich: Wayne State University
Vo Thanh Phat: HCMC University of Education
Dat Ba Tran: Wayne State University

Journal of Global Optimization, 2023, vol. 86, issue 1, No 5, 93-122

Abstract: Abstract The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of second-order subdifferentials of nonsmooth functions with employing the machinery of second-order variational analysis and generalized differentiation. First we develop a globally superlinearly convergent damped Newton-type algorithm for the class of continuously differentiable functions with Lipschitzian gradients, which are nonsmooth of second order. Then we design such a globally convergent algorithm to solve a structured class of nonsmooth quadratic composite problems with extended-real-valued cost functions, which typically arise in machine learning and statistics. Finally, we present the results of numerical experiments and compare the performance of our main algorithm applied to an important class of Lasso problems with those achieved by other first-order and second-order optimization algorithms.

Keywords: Variational analysis and nonsmooth optimization; Damped Newton methods; Global convergence; Tilt stability of minimizers; Superlinear convergence; Lasso problems; Primary: 49J52; 49J53; secondary: 90C30; 90C53 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-022-01248-7

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