Identifying an optimal basis for a linear programming problem is a challenging learning task. Traditionally, an optimal basis is obtained via the iterative simplex method which improves from the current basic feasible...
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Identifying an optimal basis for a linear programming problem is a challenging learning task. Traditionally, an optimal basis is obtained via the iterative simplex method which improves from the current basic feasible solution to the adjacent one until it reaches optimal. The obtained result is the value of the optimal solution and the corresponding optimal basis. Even though learning the optimal value is hard but learning the optimal basis is possible via deep learning. This paper presents the primal-optimal-binding LPNet that learns from massive linear programming problems of various sizes casting as all-unit-row-except-first-unit-column matrices. During the training step, these matrices are fed to the special row-column convolutional layer followed by the state-of-the-art deep learning architecture and sent to two fully connected layers. The result is the probability vector of non-negativity constraints and the original linear programming constraints at the optimal basis. The experiment shows that this LPNet achieves 99% accuracy of predicting a single binding optimal constraint on unseen test problems and Netlib problems. It identifies correctly 80% LP problems having all optimal binding constraints and faster than cplex solution time.
One way to solve very large linear programs in standard form is to apply a random projection to the constraints, then solve the projected linear program [63]. This will yield a guaranteed bound on the optimal value, a...
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Due to the difficulty of accurately predicting system reliability for many engineering structures, bounds on system reliability have received increasing attention. By dealing with structural uncertain parameters with ...
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Due to the difficulty of accurately predicting system reliability for many engineering structures, bounds on system reliability have received increasing attention. By dealing with structural uncertain parameters with an ellipsoid model, a linear programming-based non-probabilistic reliability bounds method is proposed in this paper for series systems. In this research, a linear programming model is first established, and then several strategies are proposed to simplify the model by removing zero design variables. Three numerical examples are presented to demonstrate the feasibility and validity of the proposed method.
Generally, the first factor in the primary consideration of the transportation of materials is to minimize and make the total cost of transport most economical. The model established in this study is applicable to eme...
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ISBN:
(数字)9781510652071
ISBN:
(纸本)9781510652071;9781510652064
Generally, the first factor in the primary consideration of the transportation of materials is to minimize and make the total cost of transport most economical. The model established in this study is applicable to emergency situations such as the spread of infectious diseases. The model considers how to help each province or region to transport the supplies that meet the demand to the destination in the shorted time, while ensuring the transportation cost as low as possible. Therefore, this paper establishes a model to simulate the situation, and proves the rationality and efficiency of the model.
Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional...
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Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional methods for the analysis of HIGS and other conewise linear systems, a method based on linear programming (LP) for constructing continuous piecewise affine (CPA) Lyapunov functions is investigated. In this paper, it is shown how linear programming can be used to prove input-to-state stability and calculate upper bounds on the L-1-gain and H-1-norm. The numerical efficiency of this CPA (LP) method will be compared to that of the CPQ (LMI) method on a numerical example involving HIGS. Copyright (c) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)
An (epsilon, delta)-DP mechanism is a mapping defined as follows. The domain of the mechanism is a finite set of objects, (also called the data points) such that a symmetric neighborhood relation over the data points ...
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ISBN:
(纸本)9798350387100;9798350387094
An (epsilon, delta)-DP mechanism is a mapping defined as follows. The domain of the mechanism is a finite set of objects, (also called the data points) such that a symmetric neighborhood relation over the data points is defined. The range of the mechanism at each data point is a distribution over another set. Further more, neighboring data points must be mapped to two distributions that are not far away. The parametric notion of distance of two distribution in terms of the parameters (epsilon, delta) in the context of privacy theory, is first introduced by D-work and her collaborators. In this paper, we study the following problem. Given a finite set D of data points, the neighboring relation, the parameters epsilon, delta, and a partial mechanism that is defined over a subset D ' subset of D, is there an extension of the mechanism defined over the entire set D that is identical to the partial mechanism on D ' and also, is (epsilon, delta)-differential private. We show that there exists an algorithm to answer this question and it runs in time that is polynomial in the input variables. Our result generalizes a result of Medard et al. about optimum mechanism extension with respect to preferential query ordering.
Battery Energy Storage Systems (BESS) are expected to play an important part in the power system of the future to meet an increasing share of the electricity demand from renewable energy sources. This paper deals with...
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ISBN:
(纸本)9798350372397;9798350372380
Battery Energy Storage Systems (BESS) are expected to play an important part in the power system of the future to meet an increasing share of the electricity demand from renewable energy sources. This paper deals with the sizing and operation optimization of a hybrid a PV system with different battery technologies, namely lithium-ion, vanadium redox flow, and sodium- sulfur batteries, to cover a specified proportion of the electricity demand. Based on PV production and electricity consumption profiles a linear optimization was executed for the whole year of 2022 with a 15-minute resolution to calculate the optimal size of PV and BESS. The hybrid systems with optimal sizing offer cost savings between 10 and 25% compared to the case where all electricity is purchased from the day-ahead market. The results also reveal that PV overbuilding offers a cheaper way to increase the share of the demand covered by renewables at current investment cost levels, while the implementation of BESS is only feasible at lower investment costs.
This paper integrates L1-norm structural risk minimization with L1-norm approximation error to develop a new optimization framework for solving the parameters of sparse kernel regression models, addressing the challen...
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This paper integrates L1-norm structural risk minimization with L1-norm approximation error to develop a new optimization framework for solving the parameters of sparse kernel regression models, addressing the challenges posed by complex model structures, over-fitting, and limited modeling accuracy in traditional nonlinear system modeling. The first L1-norm regulates the complexity of the model structure to maintain its sparsity, while another L1-norm is essential for ensuring modeling accuracy. In the optimization of support vector regression (SVR), the L2-norm structural risk is converted to an L1-norm framework through the condition of non-negative Lagrange multipliers. Furthermore, L1-norm optimization for modeling accuracy is attained by minimizing the maximum approximation error. The integrated L1-norm of structural risk and approximation errors creates a new, simplified optimization problem that is solved using linear programming (LP) instead of the more complex quadratic programming (QP). The proposed sparse kernel regression model has the following notable features: (1) it is solved through relatively simple LP;(2) it effectively balances the trade-off between model complexity and modeling accuracy;and (3) the solution is globally optimal rather than just locally optimal. In our three experiments, the sparsity metrics of SVs% were 2.67%, 1.40%, and 0.8%, with test RMSE values of 0.0667, 0.0701, 0.0614 (sinusoidal signal), and 0.0431 (step signal), respectively. This demonstrates the balance between sparsity and modeling accuracy.
This paper investigates the filtering design of positive complex networks in both discrete- and continuous-time contexts. A positive filtering is proposed for discrete-time complex networks. The filtering gain matrice...
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ISBN:
(纸本)9798350387780;9798350387797
This paper investigates the filtering design of positive complex networks in both discrete- and continuous-time contexts. A positive filtering is proposed for discrete-time complex networks. The filtering gain matrices are designed based on a matrix decomposition approach. All positivity and stability conditions are described in terms of linear programming. A novel positivity analysis framework is constructed for complex networks and the corresponding error systems and a gain filtering design is solved using copositive Lyapunov function. The presented filtering design approach is developed for continuous time complex networks. Finally, an example is provided to verify the validity of the proposed filtering.
This paper focuses on the event-triggered observation and control of positive complex networks with randomly occurring nonlinearities obeying a Bernoulli distribution. By utilizing observation errors and sensor measur...
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ISBN:
(纸本)9798350390780;9798350379228
This paper focuses on the event-triggered observation and control of positive complex networks with randomly occurring nonlinearities obeying a Bernoulli distribution. By utilizing observation errors and sensor measurements, an event-triggered scheme is formulated based on the form of 1-norm. An event-triggered controller is designed by using linear programming. Sufficient conditions are addressed to ensure the positivity of the lower bound of the closed-loop system. By employing a co-positive Lyapunov function, the stability of the upper bound of the closed-loop system is established. Finally, a simulation example is provided to illustrate the efficacy of the proposed design.
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