"Rural Agglomerations” and "Rural Associations of Settlements” — Possible Directions for the Development of Local Self-Government in the North-West of Russia

The problem of improving the effectiveness of local self-government in the Russian Federation is particularly complex. Geographical and historical prerequisites work against economic efficiency and proportional political representation. The concepts of rural agglomerations and rural associations of human settlements can be considered as search directions in the search for a solution to the problem of “efficiency or equality”. The North-West of Russia can be considered as an effective training ground for the development of new management approaches.

A Convex Combination between Two Different Search Directions of Conjugate Gradient Method and Application in Image Restoration

The conjugate gradient is a useful tool in solving large- and small-scale unconstrained optimization problems. In addition, the conjugate gradient method can be applied in many fields, such as engineering, medical research, and computer science. In this paper, a convex combination of two different search directions is proposed. The new combination satisfies the sufficient descent condition and the convergence analysis. Moreover, a new conjugate gradient formula is proposed. The new formula satisfies the convergence properties with the descent property related to Hestenes–Stiefel conjugate gradient formula. The numerical results show that the new search direction outperforms both two search directions, making it convex between them. The numerical result includes the number of iterations, function evaluations, and central processing unit time. Finally, we present some examples about image restoration as an application of the proposed conjugate gradient method.

Two Modified Single-Parameter Scaling Broyden–Fletcher–Goldfarb–Shanno Algorithms for Solving Nonlinear System of Symmetric Equations

In this paper, we develop two algorithms to solve a nonlinear system of symmetric equations. The first is an algorithm based on modifying two Broyden–Fletcher–Goldfarb–Shanno (BFGS) methods. One of its advantages is that it is more suitable to effectively solve a small-scale system of nonlinear symmetric equations. In contrast, the second algorithm chooses new search directions by incorporating an approximation method of computing the gradients and their difference into the determination of search directions in the first algorithm. In essence, the second one can be viewed as an extension of the conjugate gradient method recently proposed by Lv et al. for solving unconstrained optimization problems. It was proved that these search directions are sufficiently descending for the approximate residual square of the equations, independent of the used line search rules. Global convergence of the two algorithms is established under mild assumptions. To test the algorithms, they are used to solve a number of benchmark test problems. Numerical results indicate that the developed algorithms in this paper outperform the other similar algorithms available in the literature.

A Modified Scaled Spectral-Conjugate Gradient-Based Algorithm for Solving Monotone Operator Equations

This paper proposes a modified scaled spectral-conjugate-based algorithm for finding solutions to monotone operator equations. The algorithm is a modification of the work of Li and Zheng in the sense that the uniformly monotone assumption on the operator is relaxed to just monotone. Furthermore, unlike the work of Li and Zheng, the search directions of the proposed algorithm are shown to be descent and bounded independent of the monotonicity assumption. Moreover, the global convergence is established under some appropriate assumptions. Finally, numerical examples on some test problems are provided to show the efficiency of the proposed algorithm compared to that of Li and Zheng.

Generalised Pattern Search Based on Covariance Matrix Diagonalisation

Pattern Search is a family of gradient-free direct search methods for numerical optimisation problems. The characterising feature of pattern search methods is the use of multiple directions spanning the problem domain to sample new candidate solutions. These directions compose a matrix of potential search moves, that is the pattern. Although some fundamental studies theoretically indicate that various directions can be used, the selection of the search directions remains an unaddressed problem. The present article proposes a procedure for selecting the directions that guarantee high convergence/high performance of pattern search. The proposed procedure consists of a fitness landscape analysis to characterise the geometry of the problem by sampling points and selecting those whose objective function values are below a threshold. The eigenvectors of the covariance matrix of this distribution are then used as search directions for the pattern search. Numerical results show that the proposed method systematically outperforms its standard counterpart and is competitive with modern complex direct search and metaheuristic methods.

A new modification of the quasi-newton method for unconstrained optimization

<p class="MsoNormal" style="text-align: justify;"><span>In this work we propose and analyze a hybrid conjugate gradient (CG) method in which the parameter <!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1674222415"> </o:OLEObject> </xml><![endif]-->is computed as a linear combination between Hager-Zhang [HZ] and Dai-Liao [DL] parameters. We use this proposed method to modify BFGS method and to prove the positive definiteness and QN-conditions of the matrix. Theoretical trils confirm that the new search directions aredescent directions under some conditions, as well as, the new search directions areglobally convergent using strong Wolfe conditions. The numerical experiments show that the proposed method is promising and outperforms alternative similar CG-methods using Dolan-Mor'e performance profile. </span><br /><br /></p>

ETHNOSOCIOLOGICAL RESEARCH OF THE OMSK SCIENTIFIC ETHNOGRAPHIC CENTER: PROBLEMATIC AND SCIENTIFIC CONTACTS

The article analyzes the diverse activities of scientists of the Omsk scientific ethnographic center related to ethnosociological topics. The article provides data on its formation and structure identifies the main re-search directions of various peoples of Siberia and Kazakhstan in 1974-2019, and the most active scien-tific contacts with scientists from Russia.