Search results for: steepest%20descent

Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

Abstract:

Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: steepest descent, line search, iteration, running time, unconstrained optimization, convergence

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Authors: Jianhong Xiang, Hao Xiang, Linyu Wang

Abstract:

Compressed sensing (CS) has a wide range of applications in sparse signal reconstruction. Aiming at the problems of low recovery accuracy and long reconstruction time of existing reconstruction algorithms in medical imaging, this paper proposes a corrected smoothing L0 algorithm based on compressed sensing (CSL0). First, an approximate hyperbolic tangent function (AHTF) that is more similar to the L0 norm is proposed to approximate the L0 norm. Secondly, in view of the "sawtooth phenomenon" in the steepest descent method and the problem of sensitivity to the initial value selection in the modified Newton method, the use of the steepest descent method and the modified Newton method are jointly optimized to improve the reconstruction accuracy. Finally, the CSL0 algorithm is simulated on various images. The results show that the algorithm proposed in this paper improves the reconstruction accuracy of the test image by 0-0. 98dB.

Keywords: smoothed L0, compressed sensing, image processing, sparse reconstruction

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Authors: Hirofumi Miyajima, Kazuya Kishida, Noritaka Shigei, Hiromi Miyajima

Abstract:

Most of self-tuning fuzzy systems, which are automatically constructed from learning data, are based on the steepest descent method (SDM). However, this approach often requires a large convergence time and gets stuck into a shallow local minimum. One of its solutions is to use fuzzy rule modules with a small number of inputs such as DIRMs (Double-Input Rule Modules) and SIRMs (Single-Input Rule Modules). In this paper, we consider a (generalized) DIRMs model composed of double and single-input rule modules. Further, in order to reduce the redundant modules for the (generalized) DIRMs model, pruning and generative learning algorithms for the model are suggested. In order to show the effectiveness of them, numerical simulations for function approximation, Box-Jenkins and obstacle avoidance problems are performed.

Keywords: Box-Jenkins's problem, double-input rule module, fuzzy inference model, obstacle avoidance, single-input rule module

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Authors: Alexander Vaninsky

Abstract:

The objective of this paper is finding the way of economic restructuring - that is, change in the shares of sectoral gross outputs - resulting in the maximum possible increase in the gross domestic product (GDP) combined with decreases in energy consumption and CO2 emissions. It uses an input-output model for the GDP and factorial models for the energy consumption and CO2 emissions to determine the projection of the gradient of GDP, and the antigradients of the energy consumption and CO2 emissions, respectively, on a subspace formed by the structure-related variables. Since the gradient (antigradient) provides a direction of the steepest increase (decrease) of the objective function, and their projections retain this property for the functions' limitation to the subspace, each of the three directional vectors solves a particular problem of optimal structural change. In the next step, a type of factor analysis is applied to find a convex combination of the projected gradient and antigradients having maximal possible positive correlation with each of the three. This convex combination provides the desired direction of the structural change. The national economy of the United States is used as an example of applications.

Keywords: economic restructuring, input-output analysis, divisia index, factorial decomposition, E3 models

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Authors: Rajkumar Ghosh

Abstract:

Jhakri Thrust (JT) coeval of Sarahan Thrust (ST) was later considered to be part of Chaura Thrust (CT). The Main Central Thrust (MCT) delimits the southern extreme of Higher Himalaya, whereas the northern boundary defines by South Tibetan Detachment System (STDS). STDS is parallel set of north dipping extensional faults. The activation timing of MCT and STDS. MCT activated in two parts (MCT-L during 15- 0.7 Ma, and MCT-U during 25-14 Ma). Similarly, STDS triggered in two parts (STDS-L during 24-12 Ma, and STDS-U during 19-14 Ma). The activation ages for MBT and MFT. Besides, the MBT occurred during 11-9 Ma, and MFT followed as <2.5 Ma. There are two mylonitised zones (zone of S-C fabric) found under the microscope. Dynamic and bulging recrystallization and sub-grain formation was documented under the optical microscope from samples collected from these zones. The varieties of crenulated schistosity are shown in photomicrographs. In a rare and uncommon case, crenulation cleavage and sigmoid Muscovite were found together side-by-side. Recrystallized quartzo-feldspathic grains exist in between crenulation cleavages. These thin-section studies allow three possible hypotheses for such variations in crenulation cleavages. S/SE verging meso- and micro-scale box folds around Chaura might be a manifestation of some structural upliftment. Near Chaura, kink folds are visible. Prominent asymmetric shear sense indicators in augen mylonite are missing in meso-scale but dominantly present under the microscope. The main foliation became steepest (range of dip ~ 65 – 80 º) at this place. The aim of this section is to characterize the box fold and its signature in the regional geology of Himachal Himalaya. Grain Boundary Migration (GBM) associated temperature range (400–750 ºC) from microstructural studies in grain scale along Jhakri-Wangtu transect documented. Oriented samples were collected from the Jhakri-Chaura transect at a regular interval of ~ 1km for strain analysis. The Higher Himalayan Out-of-Sequence Thrust (OOST) in Himachal Pradesh is documented a decade ago. The OOST in other parts of the Himalayas is represented as a line in between MCTL and MCTU. But In Himachal Pradesh area, OOST activated the MCTL as well as in between a zone located south of MCTU. The expectations for strain variation near the OOST are very obvious. But multiple sets of OOSTs may produce a zigzag pattern of strain accumulation for this area and figure out the overprinting structures for multiple sets of OOSTs.

Keywords: Chaura Thrust, out-of-sequence thrust, Main Central Thrust, Sarahan Thrust

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