This paper focuses on the study of an original combination of the Multilevel Monte Carlo method introduced by Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56(3) (2008), pp. 607-617.] and the popular impor...
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This paper focuses on the study of an original combination of the Multilevel Monte Carlo method introduced by Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56(3) (2008), pp. 607-617.] and the popular importance sampling technique. To compute the optimal choice of the parameter involved in the importance sampling method, we rely on Robbins-Monro type stochastic algorithms. On the one hand, we extend our previous work [M. Ben Alaya, K. Hajji and A. Kebaier, Importance sampling and statistical Romberg method, Bernoulli 21(4) (2015), pp. 1947-1983.] to the Multilevel Monte Carlo setting. On the other hand, we improve [M. Ben Alaya, K. Hajji and A. Kebaier, Importance sampling and statistical Romberg method, Bernoulli 21(4) (2015), pp. 1947-1983.] by providing a new adaptive algorithm avoiding the discretization of any additional process. Furthermore, from a technical point of view, the use of the same stochastic algorithms as in [M. Ben Alaya, K. Hajji and A. Kebaier, Importance sampling and statistical Romberg method, Bernoulli 21(4) (2015), pp. 1947-1983.] appears to be problematic. To overcome this issue, we employ an alternative version of stochastic algorithms with projection (see, e.g. Laruelle, Lehalle and Pages [Optimal posting price of limit orders: learning by trading, Math. Financ. Econ. 7(3) (2013), pp. 359-403.]). In this setting, we show innovative limit theorems for a doubly indexed stochastic algorithm which appear to be crucial to study the asymptotic behaviour of the new adaptive Multilevel Monte Carlo estimator. Finally, we illustrate the efficiency of our method through applications from quantitative finance.
In this paper, we presented a Quadratic Interpolated Beetle Antennae Search (QIBAS), a variant of the Beetle Antennae Search (BAS) algorithm to solve the higher dimensional portfolio selection problem. The computation...
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In this paper, we presented a Quadratic Interpolated Beetle Antennae Search (QIBAS), a variant of the Beetle Antennae Search (BAS) algorithm to solve the higher dimensional portfolio selection problem. The computational efficiency of BAS and its probabilistic global convergence made it viable to solve real-world optimization-based problems. Despite its numerous application, it is less accurate, not scalable, and its performance deteriorates as the dimension of the problem increases. To overcome this, QIBAS integrates BAS with the robust approximation of quadratic interpolation. We employed QIBAS to a well-known finance problem known as Portfolio Selection as a testbed. Traditionally, the portfolio problem is modeled as a convex optimization problem, which is efficient to solve but inaccurate. The cardinality constrained model with higher dimensional stock data includes stringent real-world constraints. It is more accurate but computationally challenging and not tractable, making it a perfect candidate to test QIBAS. The primary goal is to minimize the risk and maximize the profit while selecting the portfolio. We included up to 250 companies in simulation and compared the results with BAS and two state-of-the-art swarm metaheuristic algorithms, i.e., Particle Swarm Optimization and Genetic algorithm. The results showed the promising performance of QIBAS in comparison with other algorithms.
We propose stochastic algorithms for solving large scale nonsmooth convex composite minimization problems. They activate at each iteration blocks of randomly selected proximity operators and achieve almost sure conver...
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ISBN:
(纸本)9789464593617;9798331519773
We propose stochastic algorithms for solving large scale nonsmooth convex composite minimization problems. They activate at each iteration blocks of randomly selected proximity operators and achieve almost sure convergence of the iterates to a solution without any regularity assumptions. Numerical applications to data analysis problems are provided.
We introduce NC-SARAH for non-convex optimization as a practical modified version of the original SARAH algorithm that was developed for convex optimization. NC-SARAH is the first to achieve two crucial performance pr...
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We introduce NC-SARAH for non-convex optimization as a practical modified version of the original SARAH algorithm that was developed for convex optimization. NC-SARAH is the first to achieve two crucial performance properties at the same time-allowing flexible minibatch sizes and large step sizes to achieve fast convergence in practice as verified by experiments. NC-SARAH has a close to optimal asymptotic convergence rate equal to existing prior variants of SARAH called SPIDER and SpiderBoost that either use an order of magnitude smaller step size or a fixed minibatch size. For convex optimization, we propose SARAH++ with sublinear convergence for general convex and linear convergence for strongly convex problems;and we provide a practical version for which numerical experiments on various datasets show an improved performance.
Uniform designs have been widely applied in engineering and sciences' innovation. When a lot of quantitative factors are investigated with as few runs as possible, a supersaturated uniform design with good overall...
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Uniform designs have been widely applied in engineering and sciences' innovation. When a lot of quantitative factors are investigated with as few runs as possible, a supersaturated uniform design with good overall and projection uniformity is needed. By combining combinatorial methods and stochastic algorithms, such uniform designs with flexible numbers of columns are constructed in this article under the wrap-around L-2-discrepancy. Compared with the existing designs, the new designs and their two-dimensional projections not only have less aberration, but also have lower discrepancy. Furthermore, some novel theoretical results on the minimum-aberration, uniform and uniform projection designs are obtained.
Abstract: Glutathione (γ-glutamyl-cysteinyl-glycine) is one of the main intracellular antioxidants that play an important role in cellular metabolism. In mammalian cells, glutathione is synthesized in two stages, the...
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This article studies the problem of decentralized optimization to minimize a finite-sum of convex cost functions over the nodes of a network where each cost function is further considered as the average of several con...
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This article studies the problem of decentralized optimization to minimize a finite-sum of convex cost functions over the nodes of a network where each cost function is further considered as the average of several constituent functions. Recalling the existing work, decentralized accelerated methods that consider improving both communication and computation efficiency have not yet been investigated. Based on this, we present an effective event-triggering decentralized accelerated stochastic gradient algorithm, namely, ET-DASG. ET-DASG leverages the event-triggering strategy for improving communication efficiency, the variance-reduction technique of SAGA for promoting computation efficiency, and the Nesterov's acceleration mechanism for the accelerated convergence. We provide a convergence analysis and show that ET-DASG with well-selected constant step-size can converge in the mean to the exact optimal solution. At the same time, linear convergence rate is achieved if each constituent function is strongly convex and smooth due to the adoption of gradient-tracking scheme. Under certain conditions, we prove that for each node the time interval between two successive triggering instants is larger than the iteration interval. Finally, simulation results also confirm the appealing performance of ET-DASG.
Recent trends indicate the rapid growth of nature-inspired techniques in the field of optimization. Salp Swarm algorithm (SSA) is a recently introduced stochastic algorithm that is inspired by the navigational capabil...
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Recent trends indicate the rapid growth of nature-inspired techniques in the field of optimization. Salp Swarm algorithm (SSA) is a recently introduced stochastic algorithm that is inspired by the navigational capability and foraging behavior of Salps. However, classical SSA gives unsatisfactory results on higher dimension problems depicting poor convergence rate. The search process of SSA lacks exploration and exploitation resulting in convergence inefficiency. This paper proposes a strategy based on the weighted distance position update called Weighted Salp Swarm algorithm (WSSA) to enhance the performance and convergence rate of the SSA. The proposed WSSA is validated using different benchmark functions and analyzed against seven different stochastic algorithms. The validation results confirmed enhanced performance and convergence rate of WSSA. Moreover, the proposed variant is applied for optimal sensor deployment task. WSSA approach is applied on probabilistic sensor model to maximize coverage and radio energy model to minimize energy consumption. This strategy is a trade-off between coverage and energy efficiency of the sensor network. It was observed that WSSA algorithm outperformed all the other stochastic algorithms in optimizing coverage and energy efficiency of Wireless Sensor Network (WSN).(c) 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).
Smartgrids integrate information technologies. Their concept is based on the intelligent management of intermittent renewable energies, using bidirectional communication tools between production and consumption throug...
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The present study investigates the effects of pitting corrosion and welding, both independently and combined, on the buckling and post-buckling behaviour of extruded aluminium panels. For this purpose, a finite elemen...
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ISBN:
(纸本)9780791886847
The present study investigates the effects of pitting corrosion and welding, both independently and combined, on the buckling and post-buckling behaviour of extruded aluminium panels. For this purpose, a finite element model of an aluminium panel made of AA6082-T6 extruded profiles is first developed without having the pitting corrosion and welding effects considered. Then, this finite element model is upgraded to account for the welding effects. This is followed by the validation of the upgraded model against the experimental data obtained from the literature. After the model validation, a hierarchical stochastic algorithm is utilised to simulate the pitting corrosion attack as geometrical defects distributed on the surface of both finite element models, with and without the welding-induced imperfections. Two different corrosion scenarios are considered. In the first scenario, the plating is corroded while the stiffeners remain intact. In the second scenario, the plating is intact, and the stiffeners contain pitting corrosion defects. The corroded parts are modelled with solid, hexahedral elements while shell elements are employed elsewhere. The effect of element type on the numerical results is discussed. Ultimately, the results obtained from the finite element models with and without corrosion and welding effects are compared in terms of ultimate strength, post-buckling response and stress/strain distribution.
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