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Some theoretical limitations of second-order algorithms for smooth constrained optimization

Gabriel Haeser (ghaeser***at***ime.usp.br)

Abstract: In second-order algorithms, we investigate the relevance of the constant rank of the full set of active constraints in ensuring global convergence to a second-order stationary point. We show that second-order stationarity is not expected in the non-constant rank case if the growth of the so-called tangent multipliers, associated with a second-order complementarity measure, is not controlled. We then investigate how these parameters should be controlled in order for the second-order information to remain present. Since no algorithm directly controls the growth of tangent multipliers, we argue that there is a theoretical limitation of present algorithms in finding second-order stationary points beyond the constant rank case.

Keywords: Global convergence, Second-order algorithms, Constant rank, Second-order optimality conditions

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 01/30/2017
Entry Accepted: 01/30/2017
Entry Last Modified: 02/02/2018

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