scholarly journals Generalized Majorization-Minimization for Non-Convex Optimization

2019 ◽  
Author(s):  
Hu Zhang ◽  
Pan Zhou ◽  
Yi Yang ◽  
Jiashi Feng
Keyword(s):  
Logistic Regression ◽  
Convex Optimization ◽  
Empirical Studies ◽  
Asymptotic Convergence ◽  
Mm Algorithm ◽  
Convex Problems ◽  
Fast Convergence Rate ◽  
Surrogate Function ◽  
Finite Sum ◽  
Theoretical Results

Majorization-Minimization (MM) algorithms optimize an objective function by iteratively minimizing its majorizing surrogate and offer attractively fast convergence rate for convex problems. However, their convergence behaviors for non-convex problems remain unclear. In this paper, we propose a novel MM surrogate function from strictly upper bounding the objective to bounding the objective in expectation. With this generalized surrogate conception, we develop a new optimization algorithm, termed SPI-MM, that leverages the recent proposed SPIDER for more efficient non-convex optimization. We prove that for finite-sum problems, the SPI-MM algorithm converges to an stationary point within deterministic and lower stochastic gradient complexity. To our best knowledge, this work gives the first non-asymptotic convergence analysis for MM-alike algorithms in general non-convex optimization. Extensive empirical studies on non-convex logistic regression and sparse PCA demonstrate the advantageous efficiency of the proposed algorithm and validate our theoretical results.

scholarly journals LOGISTIC REGRESSION FOR EMPIRICAL STUDIES OF MULTIVARIATE SELECTION

Evolution ◽  
1998 ◽  
Vol 52 (6) ◽  
pp. 1564-1571 ◽  
Author(s):  
Fredric J. Janzen ◽  
Hal S. Stern
Keyword(s):  
Logistic Regression ◽  
Empirical Studies

scholarly journals Pengaruh Elemen-Elemen Fraud Pentagon Terhadap Kecurangan Laporan Keuangan

2020 ◽  
Vol 2 (4) ◽  
pp. 3405-3418
Author(s):  
Alfamet Randa ◽  
Sany Dwita
Keyword(s):  
Logistic Regression ◽  
Regression Analysis ◽  
Data Analysis ◽  
Financial Reporting ◽  
Stock Exchange ◽  
Empirical Studies ◽  
Sampling Technique ◽  
Fraudulent Financial Reporting ◽  
Real Estate Sector ◽  
Final Sample

This study aims to determine the effect of pentagon fraud’s theory in detecting fraudulent financial reporting empirical studies on companies in property and real estate sector in Indonesia listed on the Stock Exchange in 2014-2018. The sampling technique used purposive sampling with the final sample of 18 companies. Data analysis used in this research is logistic regression analysis. The result of this research showed that : Pressure (ROA), Opportunity (BDOUT), Competence (DCHANGE) and Arogance (CEOPIC) have no significant effect on fraudulent financial reporting. While the Rationalization (Change of Auditor) has a significant effect on fraudulent financial reporting.

Segregation of Heterogeneous Robotics Swarms via Convex Optimization

2016 ◽  
Author(s):  
Victoria Edwards ◽  
Paulo Rezeck ◽  
Luiz Chaimowicz ◽  
M. Ani Hsieh
Keyword(s):  
Convex Optimization ◽  
Division Of Labor ◽  
Optimization Approach ◽  
Control Methods ◽  
Natural Phenomena ◽  
The Past ◽  
Robotic Swarms ◽  
Theoretical Results

The division of labor amongst a heterogeneous swarm of robots increases the range and sophistication of the tasks the swarm can accomplish. To efficiently execute a task the swarm of robots must have some starting organization. Over the past decade segregation of robotic swarms has grown as a field of research drawing inspiration from natural phenomena such as cellular segregation. A variety of different approaches have been undertaken to devise control methods to organize a heterogeneous swarm of robots. In this work, we present a convex optimization approach to segregate a heterogeneous swarm into a set of homogeneous collectives. We present theoretical results that show our approach is guaranteed to achieve complete segregation and validate our strategy in simulation and experiments.

scholarly journals A perturbation view of level-set methods for convex optimization

2020 ◽  
Vol 14 (8) ◽  
pp. 1989-2006
Author(s):  
Ron Estrin ◽  
Michael P. Friedlander
Keyword(s):  
Convex Optimization ◽  
Level Set ◽  
Level Set Methods ◽  
Sufficient Conditions ◽  
Strong Duality ◽  
Necessary Condition ◽  
Root Finding ◽  
Convex Problems ◽  
Level Set Approach ◽  
Slater's Constraint Qualification

Abstract Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again across a range of algorithms for convex problems. Here we demonstrate that strong duality is a necessary condition for the level-set approach to succeed. In the absence of strong duality, the level-set method identifies $$\epsilon $$ ϵ -infeasible points that do not converge to a feasible point as $$\epsilon $$ ϵ tends to zero. The level-set approach is also used as a proof technique for establishing sufficient conditions for strong duality that are different from Slater’s constraint qualification.

Extracting Knowledge from Neural Networks

2011 ◽  
pp. 188-196 ◽  
Author(s):  
Christie M. Fuller ◽  
Rick L. Wilson
Keyword(s):  
Neural Networks ◽  
Logistic Regression ◽  
Discriminant Analysis ◽  
Classification Accuracy ◽  
Empirical Studies ◽  
Inductive Learning ◽  
Learning Systems ◽  
Great Promise ◽  
Classifier Systems ◽  
Case Classification

Neural networks (NN) as classifier systems have shown great promise in many problem domains in empirical studies over the past two decades. Using case classification accuracy as the criteria, neural networks have typically outperformed traditional parametric techniques (e.g., discriminant analysis, logistic regression) as well as other non-parametric approaches (e.g., various inductive learning systems such as ID3, C4.5, CART, etc.).

The impact of intellectual capital on start-up expectations

2016 ◽  
Vol 17 (4) ◽  
pp. 654-674 ◽  
Author(s):  
Diego Matricano
Keyword(s):  
Logistic Regression ◽  
Intellectual Capital ◽  
Regression Models ◽  
Empirical Studies ◽  
Binary Logistic Regression ◽  
Research Trend ◽  
Content Type ◽  
Logistic Regression Models ◽  
Start Up ◽  
The Impact

Purpose According to an emerging research trend, which seeks to apply the concept of intellectual capital (IC) to the field of entrepreneurship, the purpose of this paper is to test whether IC can affect the start-up expectations of aspiring entrepreneurs. Design/methodology/approach Binary logistic regression models, based on empirical data derived from the Global Entrepreneurship Monitor website and referring to Italy over the years 2005-2010, are used to test the influence of IC (comprising human, structural and relational capital) on start-up expectations. Findings Binary logistic regression models reveal robust results. Human, structural and relational capitals affect start-up expectations in Italy. Only in 2010 did structural capital fail to do so. Research limitations/implications This study has three main limitations. The first concerns the need for further research to confirm the influence of IC on start-up expectations. The second concerns in-depth, more exhaustive analyses that cannot be carried out due to the use of second- hand data. The third deals with the reference only to Italy, over a limited time-span (2005-2010). Originality/value To the best knowledge of the author, this is one of the first empirical studies that investigate whether IC can affect start-up expectations. Results revealed by the regression models might steer other scholars’ interest toward this research path (linking IC and entrepreneurship) that has not yet been properly considered.

scholarly journals Distributed convex optimization via proportional-integral-differential algorithm

2021 ◽  
pp. 002029402110293
Author(s):  
Wei Zhu ◽  
Haibao Tian
Keyword(s):  
Convex Optimization ◽  
Utility Function ◽  
Convex Optimization Problem ◽  
Proportional Integral ◽  
Locally Lipschitz ◽  
Differential Algorithm ◽  
Distributed Convex Optimization ◽  
The Individual ◽  
Local Utility Functions ◽  
Theoretical Results

This paper studies the distributed convex optimization problem, where the global utility function is the sum of local cost functions associated to the individual agents. Only using the local information, a novel continuous-time distributed algorithm based on proportional-integral-differential (PID) control strategy is proposed. Under the assumption that the global utility function is strictly convex and local utility functions have locally Lipschitz gradients, the exponential convergence of the proposed algorithm is established with undirected and connected graph among these agents. Finally, numerical simulations are presented to illustrate the effectiveness of theoretical results.

scholarly journals Accelerated Incremental Gradient Descent using Momentum Acceleration with Scaling Factor

2019 ◽  
Author(s):  
Yuanyuan Liu ◽  
Fanhua Shang ◽  
Licheng Jiao
Keyword(s):  
Gradient Descent ◽  
Linear Convergence ◽  
Strongly Convex ◽  
Convex Problems ◽  
Accelerated Methods ◽  
Gradient Descent Methods ◽  
Gradient Descent Algorithm ◽  
Oracle Complexity ◽  
Incremental Gradient Descent ◽  
Theoretical Results

Recently, research on variance reduced incremental gradient descent methods (e.g., SAGA) has made exciting progress (e.g., linear convergence for strongly convex (SC) problems). However, existing accelerated methods (e.g., point-SAGA) suffer from drawbacks such as inflexibility. In this paper, we design a novel and simple momentum to accelerate the classical SAGA algorithm, and propose a direct accelerated incremental gradient descent algorithm. In particular, our theoretical result shows that our algorithm attains a best known oracle complexity for strongly convex problems and an improved convergence rate for the case of n>=L/\mu. We also give experimental results justifying our theoretical results and showing the effectiveness of our algorithm.

scholarly journals MOTIVACIONES PARA ACCIONES DE RSE EN RESORTS EN BRASIL

2016 ◽  
Author(s):  
Claudio Alexandre Souza ◽  
Jakson Renner Rodrigues Soares ◽  
María Dolores Sánchez-Fernández
Keyword(s):  
Corporate Social Responsibility ◽  
Social Responsibility ◽  
Social Relations ◽  
Empirical Studies ◽  
Tourism Product ◽  
Environment Variables ◽  
Corporate Social ◽  
Theoretical Results

El objetivo de este artículo es presentar un estudio sobre las motivaciones que impulsan a un resort a implementar acciones de responsabilidad social empresarial (RSE), teniendo como base las variables del entorno, los stakeholders y las dimensiones de la sostenibilidad. Este trabajo es el resultado de una investigación bibliográfica procedente de la revisión de artículos y bibliografía sobre los resorts y RSE, principalmente en lo que se refiere a sus respectivas motivaciones. Para la sistematización de este estudio se creó y se utilizó la Matriz de Análisis de la Responsabilidad Social Empresarial (MARSE) integrando las variables del entorno utilizadas en esta investigación. Los resultados evidencian motivaciones sistematizadas, pero estas se comportan de manera única debido a la singularidad del producto turístico resorts y a la amplitud de relaciones sociales que los mismos poseen con sus respectivos stakeholders. Tanto la MARSE, creada para este estudio, como las conclusiones obtenidas, sirven como referencia para la realización de futuros estudios empíricos acerca de las motivaciones de la implementación de la RSE en resorts. La MARSE puede ser considerada como una forma original de analizar el área RSE, debido a la posibilidad de sistematización.ABSTRACTThe purpose of the article is to present a theoretical essay about the motivations that drive a resort the achievements actions of corporate social responsibility, based on environment variables, stakeholders and dimensions of sustainability. This theoretical essay is the result of bibliographic research in journals and bibliographies on resorts and corporate social responsibility, especially regarding their respective motivations. To systematize this test was created and used the Corporate Social Responsibility Analysis Matrix (MARSE) integrating the variables analyzed in this study. The theoretical results are taken by reference motivations already systematized, however they behave in a unique way in this study by the tourism product uniqueness resorts and the extent of social relations that they have towards their respective stakeholders. Both MARSE created for this study, as the conclusions serve as a reference for future specific and empirical studies on CSR motivations resorts. The MARSE can be considered as a unique way to carry out analyzes in the CSR area, it enables the systematic.

scholarly journals GS-OPT: A new fast stochastic algorithm for solving the non-convex optimization problem

2020 ◽  
Vol 9 (2) ◽  
pp. 183
Author(s):  
Xuan Bui ◽  
Nhung Duong ◽  
Trung Hoang
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Latent Dirichlet Allocation ◽  
Stochastic Algorithm ◽  
Inference Problem ◽  
Theoretical Understanding ◽  
Convex Optimization Problem ◽  
Discrete Probability ◽  
Convex Problems ◽  
Posterior Inference

<p>Non-convex optimization has an important role in machine learning. However, the theoretical understanding of non-convex optimization remained rather limited. Studying efficient algorithms for non-convex optimization has attracted a great deal of attention from many researchers around the world but these problems are usually NP-hard to solve. In this paper, we have proposed a new algorithm namely GS-OPT (General Stochastic OPTimization) which is effective for solving the non-convex problems. Our idea is to combine two stochastic bounds of the objective function where they are made by a commonly discrete probability distribution namely Bernoulli. We consider GS-OPT carefully on both the theoretical and experimental aspects. We also apply GS-OPT for solving the posterior inference problem in the latent Dirichlet allocation. Empirical results show that our approach is often more efficient than previous ones.</p>

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