A Version of Bundle Trust Region Method with Linear Programming

Shuai Liu (), Andrew C. Eberhard () and Yousong Luo ()
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Shuai Liu: South China Normal University Nanhai Campus
Andrew C. Eberhard: Royal Melbourne Institute of Technology
Yousong Luo: Royal Melbourne Institute of Technology

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 2, No 8, 639-662

Abstract: Abstract We present a general version of bundle trust region method for minimizing convex functions. The trust region is constructed by generic $$p$$ p -norm with $$p\in [1,+\infty ]$$ p ∈ [ 1 , + ∞ ] . In each iteration the algorithm solves a subproblem with a constraint involving $$p$$ p -norm. We show the convergence of the generic bundle trust region algorithm. In implementation, the infinity norm is chosen so that a linear programming subproblem is solved in each iteration. Preliminary numerical experiments show that our algorithm performs comparably with the traditional bundle trust region method and has advantages in solving large-scale problems.

Keywords: Trust region; Bundle method; Linear programming; $$p$$ p -norm; 90C25; 49J52; 65K10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02293-2

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