A feasible SQP-GS algorithm for nonconvex, nonsmooth constrained optimization

The gradient sampling (GS) algorithm for minimizing a nonconvex, nonsmooth function was proposed by Burke et al. (SIAM J Optim 15:751–779,  2005 ), whose most interesting feature is the use of randomly sampled gradients instead of subgradients. In this paper, combining the GS technique with the sequ...

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Bibliographic Details
Published in:Numerical algorithms Vol. 65; no. 1; pp. 1 - 22
Main Authors: Tang, Chun-ming, Liu, Shuai, Jian, Jin-bao, Li, Jian-ling
Format: Journal Article
Language:English
Published: Boston Springer US 01.01.2014
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Constraints
Convergence
Iterative methods
Mathematical analysis
Mathematical models
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Quadratic programming
Sampling
Sequences
Theory of Computation
Gradient sampling
49M30
Nonsmooth optimization
90C30
Feasible algorithm
Sequential quadratic programming
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:The gradient sampling (GS) algorithm for minimizing a nonconvex, nonsmooth function was proposed by Burke et al. (SIAM J Optim 15:751–779,  2005 ), whose most interesting feature is the use of randomly sampled gradients instead of subgradients. In this paper, combining the GS technique with the sequential quadratic programming (SQP) method, we present a feasible SQP-GS algorithm that extends the GS algorithm to nonconvex, nonsmooth constrained optimization. The proposed algorithm generates a sequence of feasible iterates, and guarantees that the objective function is monotonically decreasing. Global convergence is proved in the sense that, with probability one, every cluster point of the iterative sequence is stationary for the improvement function. Finally, some preliminary numerical results show that the proposed algorithm is effective.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-012-9692-5