Hybrid spectral gradient method for the unconstrained minimization problem

Cruz, William La; Noguera, Gilberto

doi:10.1007/s10898-008-9318-6

Cited by 9 publications

(3 citation statements)

References 51 publications

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“…The approach to solve this problem is an optimization method of the quasi-Newton family that approximates the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, and which is implemented in Python [68][69][70][71]. MATLAB was used to calculate the Hessian matrix [72].…”

Section: Methodsmentioning

confidence: 99%

Anthropization and Growth of the Electricity Grid as Variables for the Analysis of Urban Infrastructure

et al. 2020

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City growth goes together with the development of infrastructure, and the power network is one of the most relevant towards economic development. The study of urban infrastructure through the analysis of anthropization coupled with power network growth can produce a tool that supports sustainable infrastructure planning, both economic and environmental. The case study focuses on Ambato, Ecuador, in the period from 1950 to 2019, and assesses quantitatively the changes in the city layout and the evolution of its power network. The data are adjusted to a sigmoid-type objective function through a non-linear least squares problem, that is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Anthropization data show how the urban area grew during the study period: at the expense of agricultural land. The forecast for new power network users by 2050 yields a result of 203,630 total users with a population density of 4850 people/km 2 . The conclusion is that this type of analysis can help city planners and decision makers further understand city and infrastructure growth dynamics and produce policies that bolster sustainable city growth.Sustainability 2020, 12, 1486 2 of 17 multi-family), but also the service networks, including the power network. However, most modern Latin American cities have experienced a fragmented urban growth, through lots and suburbs, often under speculative pressure and unplanned self-construction as new land is made available and has access to service infrastructure [5].Documenting the growth of a city can be very useful if the drawings are made with further purpose than observing formal chronological aspects of the architectural background [6]. Adding other backgrounds and variables to cross evaluate and analyse gives a better understanding of unforeseen growth tendencies and brings up otherwise hidden deficiencies of the urban service networks in the different areas of the city. This information is very valuable when establishing sustainable urban planning criteria [7,8], Herce and Miró Farellons suggest five development lines to reformulate urban models from a sustainability standpoint [9]. These include relating service infrastructure with land use in order to increase efficiency.The study of anthropization together with infrastructure growth is an essential tool to assess the state of a city and determine actions to bolster its sustainability based on economic parameters (economic accessibility, production, private sector, public services, jobs); environmental parameters (agriculture, water, air, energy, environmental management, resources, waste, noise); social parameters (quality of life, environmental education, population, identity, social inclusion, participation, safety, and health); and urban parameters (equipment, street furniture, green areas, planning and management, land, transportation) [10][11][12]. In this context, urban infrastructure includes transportation networks, fresh water and sewers networks, power network, and information network, as well as the managemen...

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Section: Methodsmentioning

confidence: 99%

Anthropization and Growth of the Electricity Grid as Variables for the Analysis of Urban Infrastructure

et al. 2020

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“…On the contrary, in our new hybridize scheme, as proposed in [19], the iterative algorithm is applied to guide the search of the GA every time that the regularized L-BFGS generates an iterate x k ∈ R n , the GA looks inside a certain region that contains x k for some other point that probably improves the value of f (x k ). The framework of the new hybridize scheme is outlined in Algorithm 2.…”

Section: Procedures 1(see [19])mentioning

confidence: 99%

“…Finally, to put our new setting in the global optimization context, we present a hybrid scheme based on the genetic algorithm (GA) and the new proposed regularized L-BFGS algorithm in order to increase the chance of finding a global minima in a reasonable CPU time. Preliminary numerical results indicate that the new methodology finds efficiently and quite frequently the global minima in comparison with SGA algorithm, as proposed in [19], and the hybrid GA of the Toolbox of Global Optimization of MATLAB.…”

Section: Introductionmentioning

confidence: 99%

A new regularized limited memory BFGS-type method based on modified secant conditions for unconstrained optimization problems

Tarzanagh

Peyghami

2015

J Glob Optim

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In the framework of large-scale optimization problems, the standard BFGS method is not affordable due to memory constraints. The so-called limited-memory BFGS (L-BFGS) method is an adaption of the BFGS method for large-scale settings. However, the standard BFGS method and therefore the standard L-BFGS method only use the gradient information of the objective function and neglect function values. In this paper, we propose a new regularized L-BFGS method for solving large scale unconstrained optimization problems in which more available information from the function and gradient values are employed to approximate the curvature of the objective function. The proposed method utilizes a class of modified quasi-Newton equations in order to achieve higher order accuracy in approximating the second order curvature of the objective function. Under some standard assumptions, we provide the global convergence property of the new method. In order to provide an efficient method for finding global minima of a continuously differentiable function, a hybrid algorithm that combines a genetic algorithm (GA) with the new proposed regularized L-BFGS method has been proposed. This combination leads the iterates to a stationary point of the objective function with higher chance of being global minima. Numerical results show the efficiency and robustness of the new proposed regularized L-BFGS and its hybridized version with GA in practice.

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NPSOG: A New Hybrid Method for Unconstrained Differentiable Optimization

Lakhbab

2020

Nonlinear Systems and Complexity

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Hybrid spectral gradient method for the unconstrained minimization problem

Cited by 9 publications

References 51 publications

Anthropization and Growth of the Electricity Grid as Variables for the Analysis of Urban Infrastructure

Anthropization and Growth of the Electricity Grid as Variables for the Analysis of Urban Infrastructure

A new regularized limited memory BFGS-type method based on modified secant conditions for unconstrained optimization problems

NPSOG: A New Hybrid Method for Unconstrained Differentiable Optimization

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