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On minimization of a quadratic function with one negative eigenvalue

Minarchenko I., Khamisov O. On minimization of a quadratic function with one negative eigenvalue // Optimization Letters. 2020. DOI: 10.1007/s11590-020-01653-5 It is well known that a quadratic programming minimization problem with one negative eigenvalue is NP-hard. However, in practice one may expect such problems being not so difficult to solve. We suggest to make a single partition of the feasible set in a concave variable only so that a convex approximation of the objective function upon every...

Теги: branch-and-bound method , global optimization , parallel computing , quadratic programming , np-hard , approximate solution , computational comparisons , convex approximation , minimization problems , nonconvex quadratic programs , objective functions , partition se
Piecewise linear bounding functions in univariate global optimization

Posypkin M., Usov A., Khamisov O. Piecewise linear bounding functions in univariate global optimization // Soft Computing. 2020. 17 p. DOI: 10.1007/s00500-020-05254-3 The paper addresses the problem of constructing lower and upper estimators for univariate functions. This problem is of crucial importance in global optimization, where such bounds are used to reduce the search area. We propose to use piecewise linear estimators for bounding univariate functions and show how such estimators can be...

Теги: deterministic methods , estimators , piecewise linear functions , univariate global optimization , global optimization , algebraic expression , automated construction , bounding functions , first-order intervals , global optimization algorithm , objective functions
Interior Point Algorithms in Linear Optimization

Zorkaltsev V.I., Mokryi I.V. Interior Point Algorithms in Linear Optimization // Journal of Applied and Industrial Mathematics. Vol.12. No.1. 2018. P.191-199. DOI: 10.1134/S1990478918010179 This is a survey of the results concerning the development and study of the interior point algorithms. Some families of the direct and dual algorithms are considered. These algorithms entering the domain of feasible solutions take into account the objective function, which makes it possible to obtain the first...

Теги: central path , interior point method , linear programming , relative interior , energy engineering , interior point algorithm , interior-point method , linear optimization , objective functions , optimal solutions , polynomial optimization , optimizatio
Objective function decomposition in global optimization

... subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol.10556 LNCS. 2017. P.338-344. ISBN (print): 9783319694030. DOI: 10.1007/978-3-319-69404-7_28 In this paper we consider global optimization problems in which objective functions are explicitly given and can be represented as compositions of some other functions. We discuss an approach of reducing the complexity of the objective by introducing new variables and adding new constraints. © Springer International ...

Теги: d.c. function , decomposition , global optimization , induced constraint , optimization , global optimization problems , objective functions


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