Variational Problems: Local Methods

Izmailov, A. F.; Solodov, M. V.

doi:10.1007/978-3-319-04247-3_3

Cited by 3 publications

(1 citation statement)

References 34 publications

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“…For the class of kernels here described, the proposed method for constructing surrogate functions can also be understood as part of sequential quadratic programming (SQP) methods [64] when, for instance, the above penalties are utilized as constraints in a constrained ML estimation problem. Indeed, the general case of equality and inequality-constrained minimization problems is defined as [65]: which is solved by iteratively defining quadratic functions that approximate the objective function and the inequality constraint around a current iterate . In the same way, our proposal generates an algorithm with quadratic surrogate functions, where an auxiliary function in (18) must be constructed for f ( θ ) and/or g ( θ ) in (53).…”

Section: A Quadratic Surrogate Function For a Class Of Kernelsmentioning

confidence: 99%

A data augmentation approach for a class of statistical inference problems

et al. 2018

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We present an algorithm for a class of statistical inference problems. The main idea is to reformulate the inference problem as an optimization procedure, based on the generation of surrogate (auxiliary) functions. This approach is motivated by the MM algorithm, combined with the systematic and iterative structure of the Expectation-Maximization algorithm. The resulting algorithm can deal with hidden variables in Maximum Likelihood and Maximum a Posteriori estimation problems, Instrumental Variables, Regularized Optimization and Constrained Optimization problems. The advantage of the proposed algorithm is to provide a systematic procedure to build surrogate functions for a class of problems where hidden variables are usually involved. Numerical examples show the benefits of the proposed approach.

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Section: A Quadratic Surrogate Function For a Class Of Kernelsmentioning

confidence: 99%

A data augmentation approach for a class of statistical inference problems

et al. 2018

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Optimal non-anticipative scenarios for nonlinear hydro-thermal power systems

Periçaro

Karas

Gonzaga

et al. 2020

Applied Mathematics and Computation

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Hybrid globalization of convergence of subspace-stabilized sequential quadratic programming method

Zhurbenko

Izmailov

Uskov

2019

Tamb. Un. Rep. Ser. Nat. Tech. Sci.

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Local superlinear convergence of the stabilized sequential quadratic programming method is established under very weak assumptions not involving any constraint qualification conditions. However, all attempts to globalize convergence of this method inevitably face principal difficulties related to the behavior of this method when the iterates are still relatively far from solutions. Specifically, the stabilized sequential quadratic programming method has a tendency to generate long sequences of short steps before its superlinear convergence shows up. To that end, the so-called subspace-stabilized sequential quadratic programming method has been proposed, demonstrating better “semi-local” behavior, and hence, more suitable for development of practical algorithms on its basis. In this work we propose two techniques for hybrid globalization of convergence of this method: algorithm with backups, and algorithm with records.We provide theoretical results on convergence and rate of convergence of these algorithms, as well as some results of their numerical testing.

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Variational Problems: Local Methods

Cited by 3 publications

References 34 publications

A data augmentation approach for a class of statistical inference problems

A data augmentation approach for a class of statistical inference problems

Optimal non-anticipative scenarios for nonlinear hydro-thermal power systems

Hybrid globalization of convergence of subspace-stabilized sequential quadratic programming method

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