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Ellipticity of the electric field integral equation for absorbing media and the convergence of the Rao-Wilton-Glisson method

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2014年第1期54卷 114-122页

作者： Medvedik, M. Yu. Smirnov, Yu. G. Penza State Univ Penza 440026 Russia

The operator of the electric field integral equation is proved to be elliptic in the case of a flat screen and absorbing media. The method of quadratic forms is applied. As a result, the Rao-Wilton-Glisson method is s... 详细信息

关键词： electric field integral equation absorbing medium Rao-Wilton-Glisson method convergence of an algorithm

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convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2016年第10期56卷 1716-1731页

作者： Chernyaev, Yu. A. Kazan Natl Res Tech Univ Kazan 420111 Tatarstan Russia

The gradient projection method and Newton's method are generalized to the case of nonconvex constraint sets representing the set-theoretic intersection of a spherical surface with a convex closed set. Necessary ex... 详细信息

关键词： spherical surface convex closed set gradient projection method Newton's method necessary conditions for a local minimum convergence of an algorithm

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Numerical algorithm for Minimizing a Convex Function on the Intersection of a Smooth Surface and a Convex Compact Set

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2019年第7期59卷 1098-1104页

作者： Chernyaev, Yu. A. Kazan Natl Res Tech Univ Kazan 420111 Tatarstan Russia

A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a smooth surface and a convex compact set in finite-dimensional Euclidean space is proposed. The idea behind the algorithm is to reduce the original problem to a sequence of convex programming problems. Necessary extremum conditions are studied, and the convergence of the algorithm is analyzed.

关键词： smooth surface convex compact set convex programming problem projection onto a nonconvex set necessary conditions for a local minimum convergence of an algorithm

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Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2017年第10期57卷 1607-1615页

作者： Chernyaev, Yu. A. Kazan Natl Res Tech Univ Kazan 420111 Russia

A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a spherical surface and a convex compact set is proposed. The idea behind the algorithm is to reduce the original minimization problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.

关键词： spherical surface convex compact set convex programming problem necessary conditions for a local minimum convergence of an algorithm

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Gradient Projection Method for Optimization Problems with a Constraint in the Form of the Intersection of a Smooth Surface and a Convex Closed Set

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2019年第1期59卷 34-45页

作者： Chernyaev, Yu. A. Kazan Natl Res Tech Univ Kazan 420111 Tatarstan Russia

The gradient projection method is generalized to the case of nonconvex sets of constraints representing the set-theoretic intersection of a smooth surface with a convex closed set. Necessary optimality conditions are ... 详细信息

关键词： smooth surface convex closed set gradient projection method necessary conditions for a local minimum convergence of an algorithm

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Numerical algorithm for solving mathematical programming problems with a smooth surface as a constraint

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2016年第3期56卷 376-381页

作者： Chernyaev, Yu. A. Kazan Natl Res Tech Univ Ul Karla Marksa 10 Kazan 420111 Tatarstan Russia

A numerical algorithm for minimizing a convex function on a smooth surface is proposed. The algorithm is based on reducing the original problem to a sequence of convex programming problems. Necessary extremum conditio... 详细信息

关键词： smooth surface convex programming problem projection onto a nonconvex set necessary conditions for a local minimum convergence of an algorithm

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An extension of the gradient projection method and Newton's method to extremum problems constrained by a smooth surface

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2015年第9期55卷 1451-1460页

作者： Chernyaev, Yu. A. Kazan Typolev Natl Res Tech Univ Kazan 420111 Tatarstan Russia

The gradient projection method and Newton's method are extended to the case where the constraints are nonconvex and are represented by a smooth surface. Necessary extremum conditions and the convergence of the met... 详细信息

关键词： smooth surface gradient projection method Newton's method projection on a nonconvex set necessary condition for a local minimum convergence of an algorithm

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Numerical algorithm for Solving a Class of Optimization Problems with a Constraint in the Form of a Subset of Points of a Smooth Surface

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2022年第12期62卷 2033-2040页

作者： Chernyaev, Yu. A. Kazan Natl Res Tech Univ Kazan 420111 Tatarstan Russia

A numerical algorithm is proposed for minimizing a convex function on the set-theoretic difference between a set of points of a smooth surface and the union of finitely many convex open sets in n-dimensional Euclidean space. The idea behind the algorithm is to reduce the original problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.

关键词： smooth surface open convex set convex programming problem necessary conditions for a local minimum convergence of an algorithm

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Weakly sharp solutions and finite convergence of algorithms for a variational inequality problem

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OPTIMIZATION 2018年第2期67卷 329-340页

作者： Liu, Yina Xian Jiaotong Liverpool Univ Dept Math Sci Suzhou Peoples R China

The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using primal and dual gap functions, g and G, and also without considering gap functions, either. The subdifferential and locally Lipschitz properties of g + lambda G for lambda > 0 are first studied since they are useful for discussing weakly sharp solutions of the variational inequality. A result of finite termination of a class of algorithms for solving the variational inequality problem is also studied.

关键词： Variational inequality gap functions gateaux differentiable locally Lipschitz property weakly sharp solution error bound convergence of an algorithm

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An extension of the conditional gradient method to a class of nonconvex optimization problems

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Computational Mathematics and Mathematical Physics 2006年第4期46卷 548-553页

作者： Chernyaev, Yu.A. Kazan State University of Technology Kazan 420111 Tatarstan ul. Karla Marksa 10 Russian Federation

The conditional gradient method is extended to the case when the feasible set is the set-the-oretic difference of a certain convex set and the union of several convex sets. Necessary extremum conditions are used to pr... 详细信息

关键词： convergence of an algorithm Necessary condition for a local minimum Set-theoretic difference

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