The minimum norm Lagrange multiplier, as a type of informative Lagrange multiplier, is proposed to replace the classical shadow price when the later fails to exist. This kind of multiplier expresses the rate of cost i...
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The minimum norm Lagrange multiplier, as a type of informative Lagrange multiplier, is proposed to replace the classical shadow price when the later fails to exist. This kind of multiplier expresses the rate of cost improvement when the right-hand side of the constraints are permitted to slightly violated. However, the minimum norm Lagrange multiplier may fail to be informative in fully parametric optimization problems. In this paper, we extend the classical constraint violation condition to a general formulation, which captures the characteristics of the problem structure of nonlinear parametric programming models. Based on the generalized constraint violation condition, we provide sufficient conditions for the minimum norm Lagrange multiplier to be informative. Furthermore, we propose a kind of penalty function method to derive the informative Lagrange multiplier in fully parametric programming models, which means that the perturbations are not only on the right-hand side of the constraints. Finally, we use examples to support our theoretic results.
The COVID-19 pandemic has caused huge impacts to human health and world's econ-omy. Finding out the balance between social productions and pandemic control becomes crucial. In this paper, we first extend the SIR m...
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The COVID-19 pandemic has caused huge impacts to human health and world's econ-omy. Finding out the balance between social productions and pandemic control becomes crucial. In this paper, we first extend the SIR model by introducing two new status. We calibrate the model by 2022 Shanghai COVID-19 outbreak. The results shows compared to zero-constraint policy, under our control policy, 50 % more life can be saved at the cost of 2.13 % loss of consumptions. Our results also emphasize the importance of the dynamic nature and the timing of control policy, either a static pandemic control or a lagged pandemic control damages badly to people's livelihood and social productions. Counter factual experiments show that compared to the baseline, when a persistent high-strength control is applied, aggregate productions decreases by 57 %;when pandemic control ends too early, the death would rise by 15 %, when pandemic control starts too late, the death rises by 23 % and aggregate productions decreases by 13 %.
Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this meth...
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Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function.
In the field of fresh produce retail, vegetables generally have a relatively limited shelf life, and their quality deteriorates with time. Most vegetable varieties, if not sold on the day of delivery, become difficult...
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In their seminal paper, Hammer, Rosemberg, and Rudeanu present an algebraic approach, the Basic Algorithm (BA), for solving the Unconstrained Binary nonlinear programming Problem (UBNLP). BA sequentially eliminates va...
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In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), the cosine similarity measure of IVIFVs, ...
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In the traditional signal control design method, cycle length is calculated by Webster's (1957) approximate optimum cycle length formula and each phase's green time is distributed by the traffic demand rate ra...
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ISBN:
(纸本)9780784483565
In the traditional signal control design method, cycle length is calculated by Webster's (1957) approximate optimum cycle length formula and each phase's green time is distributed by the traffic demand rate ratio. This study develops a nonlinear programming model aimed at minimizing the average delay by calculating the delay using the traditional signal control calculation method. To verify the model, the open source traffic simulation tool SUMO which performs micro-traffic simulations, is used to simulate traffic at a four-leg intersection with signal under several assumed traffic demand scenarios. The results of applying the traditional signal control design method and the method developed in this study are compared. As a result, the method proposed in this study has a longer cycle time but shorter average delay time and shorter coefficient of variation of delay time than the traditional method for scenarios 1-3, which have higher traffic demand than the remaining scenario.
In this paper, an "Adaptive Receding Horizon Controller (ARHC)" is exemplified in the suboptimal control of a Furuta pendulum. A dynamic model of strongly overestimated inertia and friction parameters is use...
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ISBN:
(纸本)9781665444996
In this paper, an "Adaptive Receding Horizon Controller (ARHC)" is exemplified in the suboptimal control of a Furuta pendulum. A dynamic model of strongly overestimated inertia and friction parameters is used in an RHC controller to track the nominal trajectory under cost terms penalizing the control forces. The so obtained "optimized" trajectory is tracked by an adaptive controller that uses a realistic approximate dynamic model of the controlled system. Since the approximate and the actual model contain considerably smaller inertia and friction parameters than that used for optimization the cautiously optimized trajectory can be precisely tracked by the actual system without suffering from heavy force burdens. The adaptivity is guaranteed by a "Fixed Point Iteration"-based approach that in this manner easily can be combined with the mathematical framework of optimal controllers. Instead of using Lagrange multipliers, the optimization happens through explicitly applying the dynamic model in forward Euler integration. The operation of the method is exemplified via numerical simulations.
In B2B markets, value-based pricing and selling has become an important alternative to discounting. This study outlines a modeling method that uses customer data (product offers made to each current or potential custo...
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In B2B markets, value-based pricing and selling has become an important alternative to discounting. This study outlines a modeling method that uses customer data (product offers made to each current or potential customer, features, discounts, and customer purchase decisions) to estimate a mixed logit choice model. The model is estimated via hierarchical Bayes and machine learning, delivering customer-level parameter estimates. Customer-level estimates are input into a nonlinear programming next-offer maximization problem to select optimal features and discount level for customer segments, where segments are based on loyalty and discount elasticity. The mixed logit model is integrated with economic theory (the random utility model), and it predicts both customer perceived value for and response to alternative future sales offers. The methodology can be implemented to support value-based pricing and selling efforts. Contributions to the literature include: (a) the use of customer-level parameter estimates from a mixed logit model, delivered via a hierarchical Bayes estimation procedure, to support value-based pricing decisions;(b) validation that mixed logit customer-level modeling can deliver strong predictive accuracy, not as high as random forest but comparing favorably;and (c) a nonlinear programming problem that uses customer-level mixed logit estimates to select optimal features and discounts.
Metaheuristic algorithms for constrained optimization problems have become popular because of their ease of use and capability to obtain global solutions. However, these population-based algorithms can be computationa...
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