Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming View Full Text


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Article Info

DATE

2022-06-27

AUTHORS

Roberto Andreani, Gabriel Haeser, Leonardo M. Mito, C. Héctor Ramírez, Thiago P. Silveira

ABSTRACT

In Andreani et al. (Weak notions of nondegeneracy in nonlinear semidefinite programming, 2020), the classical notion of nondegeneracy (or transversality) and Robinson’s constraint qualification have been revisited in the context of nonlinear semidefinite programming exploiting the structure of the problem, namely its eigendecomposition. This allows formulating the conditions equivalently in terms of (positive) linear independence of significantly smaller sets of vectors. In this paper, we extend these ideas to the context of nonlinear second-order cone programming. For instance, for an m-dimensional second-order cone, instead of stating nondegeneracy at the vertex as the linear independence of m derivative vectors, we do it in terms of several statements of linear independence of 2 derivative vectors. This allows embedding the structure of the second-order cone into the formulation of nondegeneracy and, by extension, Robinson’s constraint qualification as well. This point of view is shown to be crucial in defining significantly weaker constraint qualifications such as the constant rank constraint qualification and the constant positive linear dependence condition. Also, these conditions are shown to be sufficient for guaranteeing global convergence of several algorithms, while still implying metric subregularity and without requiring boundedness of the set of Lagrange multipliers. More... »

PAGES

1-37

References to SciGraph publications

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  • 1984. Directional differentiability of the optimal value function in a nonlinear programming problem in SENSITIVITY, STABILITY AND PARAMETRIC ANALYSIS
  • 2003-01. Second-order cone programming in MATHEMATICAL PROGRAMMING
  • 1984. Solution point differentiability without strict complementarity in nonlinear programming in SENSITIVITY, STABILITY AND PARAMETRIC ANALYSIS
  • 2005-05. On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1982. Differential properties of the marginal function in mathematical programming in OPTIMALITY AND STABILITY IN MATHEMATICAL PROGRAMMING
  • 2011-05-06. A relaxed constant positive linear dependence constraint qualification and applications in MATHEMATICAL PROGRAMMING
  • 2006-07-26. An SQP-type algorithm for nonlinear second-order cone programs in OPTIMIZATION LETTERS
  • 2010-02-24. Constant-Rank Condition and Second-Order Constraint Qualification in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2017-04-18. On M-stationarity conditions in MPECs and the associated qualification conditions in MATHEMATICAL PROGRAMMING
  • 2006-12-01. Augmented Lagrangian methods under the constant positive linear dependence constraint qualification in MATHEMATICAL PROGRAMMING
  • 1969-11. Multiplier and gradient methods in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2018-06-25. New Constraint Qualifications and Optimality Conditions for Second Order Cone Programs in SET-VALUED AND VARIATIONAL ANALYSIS
  • 2000. Perturbation Analysis of Optimization Problems in NONE
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    http://scigraph.springernature.com/pub.10.1007/s10957-022-02056-5

    DOI

    http://dx.doi.org/10.1007/s10957-022-02056-5

    DIMENSIONS

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