The notion of the central path plays an important role in the development of most primal-dual interior-point algorithms. In this work we prove that a related notion called the quasicentral path, introduced by Argaez i...
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ISBN:
(纸本)9783031206108;9783031206115
The notion of the central path plays an important role in the development of most primal-dual interior-point algorithms. In this work we prove that a related notion called the quasicentral path, introduced by Argaez in nonlinear programming, while being a less restrictive notion it is sufficiently strong to guide the iterates towards a solution to the problem. We use a new merit function for advancing to the quasicentral path, and weighted neighborhoods as proximity measures of this central region. We present some numerical results that demonstrate the effectiveness of the algorithm.
In tabular multi-agent reinforcement learning with average-cost criterion, a team of agents sequentially interacts with the environment and observes local incentives. We focus on the case that the global reward is a s...
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ISBN:
(纸本)9781665467612
In tabular multi-agent reinforcement learning with average-cost criterion, a team of agents sequentially interacts with the environment and observes local incentives. We focus on the case that the global reward is a sum of local rewards, the joint policy factorizes into agents' marginals, and full state observability. To date, few global optimality guarantees exist even for this simple setting, as most results yield convergence to stationarity for parameterized policies in large/possibly continuous spaces. To solidify the foundations of MARL, we build upon linear programming (LP) reformulations, for which stochastic primal-dual methods yield a model-free approach to achieve optimal sample complexity in the centralized case. We develop multi-agent extensions, whereby agents solve their local saddle point problems and then perform local weighted averaging. We establish that the sample complexity to obtain near-globally optimal solutions matches tight dependencies on the cardinality of the state and action spaces, and exhibits classical scalings with respect to the network in accordance with multi-agent optimization. Experiments corroborate these results in practice.
作者:
Hladík, MilanCharles University
Faculty of Mathematics and Physics Department of Applied Mathematics Malostranské nám. 25 Prague11800 Czech Republic
This paper introduces a concept of a derivative of the optimal value function in linear programming (LP). Basically, it is the the worst case optimal value of an interval LP problem when the nominal data the data are ...
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Battery energy storage systems can be readily integrated with buildings to enhance renewable energy selfconsumptions while leveraging time-variant electricity tariffs for possible operation cost reductions. The extens...
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Battery energy storage systems can be readily integrated with buildings to enhance renewable energy selfconsumptions while leveraging time-variant electricity tariffs for possible operation cost reductions. The extensive variability in building operating conditions presents significant challenges in developing universally applicable methods for optimal controls. To ensure reliable and robust controls, this study integrates predictive control with efficient linear programming to effectively fine-tune battery controls for real-time operations. An adaptive time aggregation scheme has been proposed to streamline the optimization process by accounting for unique changes in energy balances and tariffs. Comprehensive data experiments, based on measurements from 95 unique building operation scenarios, have been conducted to quantify the control performance given different optimization formulations, varying types and levels of prediction uncertainties in building energy demands and PV generations. The results validate the value of the method proposed, leading to 11.75 %-34.63 % operation cost reductions on average, while reducing computation steps by 87.75 %-92.60 % compared with conventional linear programming approaches. The insights obtained are useful for developing flexible building control strategies with improved computation efficiency and robustness, while providing extensible optimization frameworks for buildings with various energy patterns and storage systems.
We adapt linear programming methods from sphere packings to closed hyperbolic surfaces and obtain new upper bounds on their systole, their kissing number, the first positive eigenvalue of their Laplacian, the multipli...
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In contrast to rotorcraft, fixed-wing unmanned aerial vehicles (UAVs) encounter a unique challenge in path planning due to the necessity of accounting for the turning radius constraint. This research focuses on covera...
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In contrast to rotorcraft, fixed-wing unmanned aerial vehicles (UAVs) encounter a unique challenge in path planning due to the necessity of accounting for the turning radius constraint. This research focuses on coverage path planning, aiming to determine optimal trajectories for fixed-wing UAVs to thoroughly explore designated areas of interest. To address this challenge, the linear programming-Fuzzy C-Means with Pigeon-Inspired Optimization algorithm (LP-FCMPIO) is proposed. Initially considering the turning radius constraint, a linear-programming-based model for fixed-wing UAV coverage path planning is established. Subsequently, to partition multiple areas effectively, an improved fuzzy clustering algorithm is introduced. Employing the pigeon-inspired optimization algorithm as the final step, an approximately optimal solution is sought. Simulation experiments demonstrate that the LP-FCMPIO, when compared to traditional FCM, achieves a more balanced clustering effect. Additionally, in contrast to traditional PIO, the planned flight paths display improved coverage of task areas, with an approximately 27.5% reduction in the number of large maneuvers. The experimental results provide validation for the effectiveness of the proposed algorithm.
Adversarial training provides an effective means to improve the robustness of neural networks against adversarial attacks. The nonlinear feature of neural networks makes it difficult to find good adversarial examples ...
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ISBN:
(纸本)9783031103636;9783031103629
Adversarial training provides an effective means to improve the robustness of neural networks against adversarial attacks. The nonlinear feature of neural networks makes it difficult to find good adversarial examples where project gradient descent (PGD) based training is reported to perform best. In this paper, we build an iterative training framework to implement effective robust training. It introduces the Least-Squares based linearization to build a set of affine functions to approximate the nonlinear functions calculating the difference of discriminant values between a specific class and the correct class and solves it using LP solvers by simplex methods. The solutions found by LP solvers turn out to be very close to the real optimum so that our method outperforms PGD based adversarial training, as is shown by extensive experiments on the MNIST and CIFAR-10 datasets. Especially, our methods can provide considerable robust networks on CIFAR-10 against the strong strength attacks, where the other methods get stuck and do not converge.
This paper is focused on a discrete time periodic optimal control problem. We establish linear programming based optimality conditions and present a method for the construction of near optimal controls. A numerical ex...
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This paper is focused on a discrete time periodic optimal control problem. We establish linear programming based optimality conditions and present a method for the construction of near optimal controls. A numerical example is included to demonstrate the results.(c) 2022 Elsevier B.V. All rights reserved.
We present the first method for the joint modulation of the continuous and the discrete nonlinear Fourier spectrum of finite duration signals. (C) 2022 The Author(s)
ISBN:
(纸本)9781557524669
We present the first method for the joint modulation of the continuous and the discrete nonlinear Fourier spectrum of finite duration signals. (C) 2022 The Author(s)
Infectious diseases are defined as the invasion of hazardous agents into the human body that causes injury and has the potential to spread to others. These diseases cause a considerable proportion of illnesses and dea...
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Infectious diseases are defined as the invasion of hazardous agents into the human body that causes injury and has the potential to spread to others. These diseases cause a considerable proportion of illnesses and deaths in any given community. The criteria importance through inter-criteria correlation (CRITIC) approach is used to determine the relative importance of multiple assessment criteria, whereas combinative distance-based assessment (CODAS) is a methodology used to compare and evaluate the efficacy of numerous options. The CRITIC-CODAS method is a linear programming-based tool for estimating the risks of infectious diseases. This method takes into account a number of aspects, including the disease's characteristics, the population at risk, and the available resources for prevention and treatment. The CRITIC-CODAS technique can provide valuable insights into the possible impact of an infectious disease outbreak and aid in improving decision-making regarding prevention and control measures by assessing these elements in a systematic and quantitative manner. The purpose of this work is to provide an overview of the CRITIC-CODAS technique, which is powered by a q-rung orthopair fuzzy set (q-ROFS), and its use in estimating the risk of infectious disease outbreaks. According to the case study, the infectious disease malaria has a greater possibility of spreading in the city under observation. According to the proposed method, the ranking of infectious cities given as g(3)(gimel) >-.g(4)(gimel) >-.g(5)(gimel) >-.g(2)(gimel) >-.g(1)(gimel). This implies that the likelihood of an epidemic of the infectious disease .g(3)(gimel) is higher in the city being observed. The study also addresses the approach's benefits and shortcomings and makes recommendations for further research and development. Overall, the CRITIC-CODAS approach appears to be a useful tool for better understanding infectious disease risks and guiding appropriate response tactics.
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