LMBOPT: a limited memory method for bound-constrained optimization

Recently, Neumaier and Azmi gave a comprehensive convergence theory for a generic algorithm for bound constrained optimization problems with a continuously differentiable objective function. The algorithm combines an active set strategy with a gradient-free line search along a piecewise linear search path defined by directions chosen to reduce zigzagging. This paper describes , an efficient implementation of this scheme. It employs new limited memory techniques for computing the search directions, improves by adding various safeguards relevant when finite precision arithmetic is used, and adds many practical enhancements in other details. The paper compares and several other solvers on the unconstrained and bound constrained problems from the collection and makes recommendations on which solver to use and when. Depending on the problem class, the problem dimension, and the precise goal, the best solvers are , , and .

An interior-point trust-region algorithm to solve a nonlinear bilevel programming problem

<abstract><p>In this paper, a nonlinear bilevel programming (NBLP) problem is transformed into an equivalent smooth single objective nonlinear programming (SONP) problem utilized slack variable with a Karush-Kuhn-Tucker (KKT) condition. To solve the equivalent smooth SONP problem effectively, an interior-point Newton's method with Das scaling matrix is used. This method is locally method and to guarantee convergence from any starting point, a trust-region strategy is used. The proposed algorithm is proved to be stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem.</p> <p>A global convergence theory of the proposed algorithm is introduced and applications to mathematical programs with equilibrium constraints are given to clarify the effectiveness of the proposed approach.</p></abstract>

Konvergensi Simbolik Komunitas Pageant Lovers Indonesia di Instagram

Perkembangan dunia beauty pageant di Indonesia tidak terlepas dari peran pecinta kontes kecantikan yang dikenal dengan sebutan pageant lovers. Media sosial Instagram menjadi salah satu kanal bagi komunitas pageant lovers untuk berinteraksi dan berkomunikasi, melalui akun portal pageant. Penelitian ini bertujuan untuk mengetahui konvergensi simbolik komunitas pageant lovers Indonesia di Instagram berdasarkan teori konvergensi simbolik. Metode penelitian yang digunakan adalah observasi terhadap caption dan kolom komentar pada unggahan akun portal pageant, serta wawancara dengan tiga narasumber dari tiga akun portal pageant berbeda. Hasil penelitian menunjukkan bahwa konvergensi simbolik komunitas pageant lovers muncul secara spontan dari anggotanya, dan digunakan secara luas melalui Instagram. Beberapa bentuk konvergensi simbolik yang muncul adalah mbak brownies, turun gunung, dan negara topi bundar. Dari penelitian ini, dapat disimpulkan bahwa konvergensi simbolik yang terjadi dalam komunitas pageant lovers Indonesia di Instagram sesuai dengan teori konvergensi simbolik yang ada, yakni melalui proses tema fantasi, rantai fantasi, tipe fantasi, dan visi retoris. The development of beauty pageants in Indonesia cannot be separated from the role of beauty pageant contest lovers known as pageant lovers. Instagram has become one of the channels for the pageant lovers community to interact and communicate through pageant portal accounts. This study aims to understand the symbolic convergence of the Indonesian pageant lovers community on Instagram based on symbolic convergence theory. The research method used is the observation of captions and comments on pageant portal accounts and interviews with three sources from three different pageant portal accounts on Instagram. The results showed that the symbolic convergence of the pageant lovers community emerged spontaneously from its members and was widely used through Instagram. Several forms of symbolic convergence that occurred were “mbak brownies”, “turun gunung, and “negara topi bundar”. Based on the results, it can be concluded that the symbolic convergence that occurs in the Indonesian pageant lovers community on Instagram is following the existing symbolic convergence theory through the process of fantasy themes, fantasy chains, fantasy types, and rhetorical visions.

Γ -convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems

The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a maximum a posteriori (MAP) estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse problem, seen as minimisation of the Onsager–Machlup (OM) functional of the posterior measure. An open problem in the stability analysis of inverse problems is to establish a relationship between the convergence properties of solutions obtained by the variational approach and by the Bayesian approach. To address this problem, we propose a general convergence theory for modes that is based on the Γ-convergence of OM functionals, and apply this theory to Bayesian inverse problems with Gaussian and edge-preserving Besov priors. Part II of this paper considers more general prior distributions.

A SIMPLE NONPARAMETRIC APPROACH FOR ESTIMATION AND INFERENCE OF CONDITIONAL QUANTILE FUNCTIONS

In this paper, we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy to implement and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the check-function-based estimator in terms of estimation mean squared error. The bootstrap confidence bands yield adequate coverage probabilities. An empirical example uses a dataset of Canadian high school graduate earnings, illustrating the usefulness of the proposed method in applications.

THE INTERNET AS A DETERMINING FACTOR IN ECONOMIC CONVERGENCE ACROSS COUNTRIES

This paper examines whether the Internet is a determining factor in explaining economic growth and convergence across countries when it acts as a channel of information and knowledge diffusion. Literature has identified around 140 possible growth factors, therefore given the contradictory results obtained from previous empirical studies it is crucial we understand the actual role of the Internet. Using the conditional convergence theory and a Bayesian panel data model averaging method from a sample of 100 countries between 1994 and 2017, our results demonstrate that an increase in access to the Internet is a non-determinant factor in economic convergence, being its probability of inclusion in the true growth model conditioned by the regressors included in the estimates and the time span analysed.

Un algoritmo global con jacobiano suavizado para problemas de complementariedad no lineal

In this paper, we use the smoothing Jacobian strategy to propose a new algorithm for solving complementarity problems based on its reformulation as a nonsmooth system of equations. This algorithm can be seen as a generalization of the one proposed in [18]. We develop its global convergence theory and under certain assumptions, we demonstrate that the proposed algorithm converges locally and, q-superlinearly or q-quadratically to a solution of the problem. Some numerical experiments show a good performance of this algorithm.

A Fantasy Theme Analysis of Chinese Rhetorical Vision on Xinjiang Cotton Incident

At the end of March 2021, some international brands and international organizations boycotted Xinjiang cotton and related products in their commercial activities, which aroused great indignation among people from all walks of life in China, and people had come forward to stand up for Xinjiang as well as Xinjiang cotton. This paper lays emphasis on the response of Chinese people to the Xinjiang cotton incident and commits to analyze what and how the fantasy themes are able to achieve with regards to the creation of rhetorical visions within contexts of symbolic convergence theory.

Basic convergence theory for the network element method

A recent paper introduced the network element method (NEM) where the usual mesh was replaced by a discretization network. Using the associated network geometric coefficients and following the virtual element framework, a consistent and stable numerical scheme was proposed. The aim of the present paper is to derive a convergence theory for the NEM under mild assumptions on the exact problem. We also derive basic error estimates, which are sub-optimal in the sense that we have to assume more regularity than usual.

THE INFLUENCE OF PERSONALITY AND SCHOOL ENVIRONMENT ON STUDENTS’ MORAL: A REVIEW ON INTERNATIONAL SCHOOL USING CONVERGENCE THEORY

Moral formation begins with the personality of the individual and the environmental factors around the individual. Consequently, an individual's propensity to be good or bad depends on internal and external factors that motivate him or her to act through his or her conduct. It is necessary to create a situation that may lead to the application of good moral values to students by a conducive education. This can ensure a motivated generation committed to fulfilling their responsibilities to themselves, their families, their peers, society and the country. This study uses Convergence Theory to examine the extent of the influence of personality and school environment in shaping the morals of Malaysian students who attend international schools in the Klang Valley.