Improved Newton’s method without direct function evaluations

Malihoutsaki, Eleftheria N.; Nikas, Ioannis A.; Grapsa, T. N.

doi:10.1016/j.cam.2008.07.013

Cited by 4 publications

(5 citation statements)

References 22 publications

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“…which has also been used in [16] and ' i (y k ) as given in the previous subsection. By using Taylor's formula, the linear approximations of g i (x), for i 2 I r , around the current point x k , lead to the following linear equations:…”

Section: Optimization 5 987mentioning

confidence: 99%

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A modified Newton direction for unconstrained optimization

Grapsa

2012

Optimization

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In this article, a modification on Newton's direction for solving problems of unconstrained optimization is presented. As it is known, a major disadvantage of Newton's method is its slowness or non-convergence for the initial point not being close to optima's neighbourhood. The proposed method generally guarantees the decrement of the norm of the gradient or the value of the objective function at every iteration, contributing to the efficiency of Newton's method. The quadratic convergence of the proposed iterative scheme and the enlargement of the radius of convergence area are proved. The proposed algorithm has been implemented and tested on several well-known test functions.

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Section: Optimization 5 987mentioning

confidence: 99%

“…At this point, we describe a way of extracting such points, which are named pivot points. More details on them can be found in [9,11,14,16]. …”

Section: Algorithm 1 the Framework Of New Direction Via An Approximatmentioning

confidence: 99%

A modified Newton direction for unconstrained optimization

Grapsa

2012

Optimization

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“…. In order to obtain a diminishing direction, each component of q(x k ) must take the minimum value, and the approximation q i (x k ) of the gradient component g i (x k ) are constructed by selecting an auxiliary point from the zero contour of g i (x k ) which are named pivot point [31], [32]. A gradient component g i (x k ) corresponds to the pivot point x k i of g i (x).…”

Section: B Cag (Componentwise Approximated Gradient) Directionmentioning

confidence: 99%

Energy-Saving Measurement in LoRaWAN-Based Wireless Sensor Networks by Using Compressed Sensing

Shi

2020

IEEE Access

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In modern monitoring systems, it is essential to deploy sensor nodes and deliver related data to the information center. Wireless sensor networks (WSNs) usually work in harsh environments with vibration, temperature variations, noise, humidity, and so on. The batteries of sensor nodes are always not replaceable because of difficult access. Most of existing literature tries to prolong network lifetime by improving sleep scheduling strategies and deployment methods, independently or jointly. However, the congenital defects of mesh network can't be avoided completely. To overcome the technology challenges, this paper develops a LoRaWAN-based WSN and investigates its energy efficient scheduling method. Firstly, the basics and the limits of LoRaWAN are introduced and the feasibility and the considerations of LoRaWAN-based star wireless sensor network are discussed. Secondly, an improved compressed sensing algorithm named ISL0 (improved SL0) is proposed for network data reconstruction and compressed sensing algorithm can reduce the number of LoRa nodes transmitting data packets to avoid collision and latency. Thirdly, a sleep schedule method is proposed to reliably monitor environment data and device operating status. By using the proposed method, not only the abnormal information can be detected on time, but also the overall network data can be recorded termly. Simulation and measurement results verify all nodes have same power level at different times, and the network lifetime is maximized. INDEX TERMS WSNs, LoRa, LoRaWAN, energy efficient scheduling, compressed sensing.

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“…If the number of cases when s k is defined using ( 15) is finite, that is, s k is defined by ( 14) for all sufficiently large k, then the proof follows from Theorem 2.1 in view of (12). Assume that there is a subsequent k m → ∞ such that…”

Section: Global Convergencementioning

confidence: 99%

“…This method is one of the most popular methods due to its attractive quadratic convergence, but it depends on the initial point and sometimes the computation of the inverse of the Hessian could be time consuming [18]. A number of different modified Newton methods have been introduced to improve the performance of the Newton method [1,[8][9][10]12]. However, the global convergence of these methods are not always guaranteed.…”

Section: Introductionmentioning

confidence: 99%

Globally convergent algorithms for solving unconstrained optimization problems

2012

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New algorithms for solving unconstrained optimization problems are presented based on the idea of combining two types of descent directions: the direction of anti-gradient and either the Newton or Quasi-Newton directions. The use of latter directions allows one to improve the convergence rate. Global and superlinear convergence properties of these algorithms are established. Numerical experiments using some unconstrained test problems are reported. Also the proposed algorithms are compared with some existing similar methods using results of experiments. This comparison demonstrates the efficiency of the proposed combined methods.

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Improved Newton’s method without direct function evaluations

Cited by 4 publications

References 22 publications

A modified Newton direction for unconstrained optimization

A modified Newton direction for unconstrained optimization

Energy-Saving Measurement in LoRaWAN-Based Wireless Sensor Networks by Using Compressed Sensing

Globally convergent algorithms for solving unconstrained optimization problems

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