On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems [PDF]
Entropy, 2021 This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the ...
Agnieszka Prusińska +2 more
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Incorporating the Soil Gas Gradient Method and Functional Genes to Assess the Natural Source Zone Depletion at a Petroleum-Hydrocarbon-Contaminated Site of a Purification Plant in Northwest China [PDF]
Life, 2022 An increasing number of studies have demonstrated that natural source zone depletion (NSZD) in the vadose zone accounts for the majority (90%~99%) of the natural attenuation of light non-aqueous phase liquid (LNAPL).
Zhuo Ning +5 more
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Toward Communication Efficient Adaptive Gradient Method [PDF]
Foundations of Data Science Conference, 2020 In recent years, distributed optimization is proven to be an effective approach to accelerate training of large scale machine learning models such as deep neural networks. With the increasing computation power of GPUs, the bottleneck of training speed in
Xiangyi Chen, Xiaoyun Li, P. Li
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Gradient Convergence in Gradient methods with Errors [PDF]
SIAM Journal on Optimization, 2000 Summary: We consider the gradient method \(x_{t+1}=x_t+\gamma_t(s_t+w_t)\), where \(s_t\) is a descent direction of a function \(f:{\mathfrak R}^n\to{\mathfrak R}\) and \(w_t\) is a deterministic or stochastic error. We assume that \(\nabla f\) is Lipschitz continuous, that the stepsize \(\gamma_t\) diminishes to 0, and that \(s_t\) and \(w_t\) satisfy
Dimitri P. Bertsekas, John N. Tsitsiklis
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A Potential Framework for Allocating National Park Service Budgets
Frontiers in Forests and Global Change, 2022 The US Department of Interior, including the National Park Service (NPS), has interest in developing a national fire budgeting process that reflects and promotes program (fuels and preparedness) efficiencies while being transparent, fair, stable, and ...
Douglas B. Rideout +3 more
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On penalty-based bilevel gradient descent method [PDF]
Mathematical programming, 2023 Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement learning.
Han Shen, Tianyi Chen
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Optimization of a fractional Mayer problem - existence of solutions, maximum principle, gradient methods [PDF]
Opuscula Mathematica, 2014 In the paper, we study a linear-quadratic optimal control problem of Mayer type given by a fractional control system. First, we prove a theorem on the existence of a solution to such a problem. Next, using the local implicit function theorem, we derive a
Dariusz Idczak, Stanislaw Walczak
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Robust Algorithm Software for NACA 4-Digit Airfoil Shape Optimization Using the Adjoint Method
Applied Sciences, 2023 Optimizing the aerodynamic shape of an airfoil is a critical concern in the aviation industry. The introduction of flexible airfoils has allowed the shape of the airfoil to vary, depending on the flight conditions. Therefore, in this study, we propose an
Naser Tanabi +3 more
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Proximal Gradient Method for Solving Bilevel Optimization Problems
Mathematical and Computational Applications, 2020 In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems.
Seifu Endris Yimer +2 more
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A New Adaptive Gradient Method with Gradient Decomposition
CoRR, 2021 Adaptive gradient methods, especially Adam-type methods (such as Adam, AMSGrad, and AdaBound), have been proposed to speed up the training process with an element-wise scaling term on learning rates. However, they often generalize poorly compared with stochastic gradient descent (SGD) and its accelerated schemes such as SGD with momentum (SGDM).
Zhou Shao, Tong Lin
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