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Study of incompatibility or near compatibility of bivariate discrete conditional probability distributions through divergence measures

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2015年第1期85卷 117-130页

作者： Ghosh, Indranil Balakrishnan, N. Austin Peay State Univ Dept Math & Stat Clarksville TN 37044 USA McMaster Univ Dept Math & Stat Hamilton ON Canada King Abdulaziz Univ Dept Stat Jeddah 21413 Saudi Arabia

Consider a two-dimensional discrete random variable (X, Y) with possible values 1, 2, horizontal ellipsis , I for X and 1, 2, horizontal ellipsis , J for Y. For specifying the distribution of (X, Y), suppose both conditional distributions, of X given Y and of Y given X, are provided. Under this setting, we present here different ways of measuring discrepancy between incompatible conditional distributions in the finite discrete case. In the process, we also suggest different ways of defining the most nearly compatible distributions in incompatible cases. Many new divergence measures are discussed along with those that are already known for determining the most nearly compatible joint distribution P. Finally, a comparative study is carried out between all these divergence measures as some examples.

关键词： linear programming iterative algorithm non-linear programming divergence measures epsilon-compatibility near compatibility conditional specification incompatible conditionals

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NEW ARC ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

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MATHEMATICAL programming 1978年第1期15卷 36-52页

作者： ZANG, I Faculty of Management Tel Aviv University Tel Aviv Israel

The gradient path of a real valued differentiable function is given by the solution of a system of differential equations. For a quadratic function the above equations are linear, resulting in a closed form solution. A quasi-Newton type algorithm for minimizing ann-dimensional differentiable function is presented. Each stage of the algorithm consists of a search along an arc corresponding to some local quadratic approximation of the function being minimized. The algorithm uses a matrix approximating the Hessian in order to represent the arc. This matrix is updated each stage and is stored in its Cholesky product form. This simplifies the representation of the arc and the updating process. Quadratic termination properties of the algorithm are discussed as well as its global convergence for a general continuously differentiable function. Numerical experiments indicating the efficiency of the algorithm are presented.

关键词： Arc Algorithms Gradientpath Algorithms non-linear programming Optimization Quasi-Newton Methods Unconstrained Optimization

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Optimization based on quasi-Monte Carlo sampling to design state estimators for non-linear systems

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OPTIMIZATION 2010年第7期59卷 963-984页

作者： Alessandri, A. Cervellera, C. Maccio, D. Sanguineti, M. Univ Genoa Dept Commun Comp & Syst Sci DIST I-16145 Genoa Italy Univ Genoa Dept Prod Engn Thermoenerget & Math Models DIPTEM I-16129 Genoa Italy Natl Res Council Italy Inst Intelligent Syst Automat ISSIA CNR I-16149 Genoa Italy

State estimation for a class of non-linear, continuous-time dynamic systems affected by disturbances is investigated. The estimator is assigned a given structure that depends on an innovation function taking on the form of a ridge computational model, with some parameters to be optimized. The behaviour of the estimation error is analysed by using input-to-state stability. The design of the estimator is reduced to the determination of the parameters in such a way as to guarantee the regional exponential stability of the estimation error in a disturbance-free setting and to minimize a cost function that measures the effectiveness of the estimation when the system is affected by disturbances. Stability is achieved by constraining the derivative of a Lyapunov function to be negative definite on a grid of points, via the penalization of the constraints that are not satisfied. Low-discrepancy sampling techniques, typical of quasi-Monte Carlo methods, are exploited in order to reduce the computational burden in finding the optimal parameters of the innovation function. Simulation results are presented to investigate the performance of the estimator in comparison with the extended Kalman filter and in dependence of the complexity of the computational model and the sampling coarseness.

关键词： state estimation input-to-state stability ridge computational models constrained optimization non-linear programming quasi-Monte Carlo methods low-discrepancy sequences

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A bioeconomic analysis of an emerald ash borer invasion of an urban forest with multiple jurisdictions

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RESOURCE AND ENERGY ECONOMICS 2014年第1期36卷 270-289页

作者： Kovacs, Kent F. Haight, Robert G. Mercader, Rodrigo J. McCullough, Deborah G. Univ Arkansas Dept Agr Econ & Agribusiness Fayetteville AR 72762 USA US Forest Serv No Res Stn St Paul MN 55108 USA Washburn Univ Dept Biol Topeka KS 66621 USA Michigan State Univ Dept Entomol E Lansing MI 48824 USA Michigan State Univ Dept Forestry E Lansing MI 48824 USA

Bio-invasions occur in management mosaics where local control affects spread and damage across political boundaries. We address two obstacles to local implementation of optimal regional control of a bio-invasion that damages public and private resources across jurisdictions: lack of local funds to protect the public resource and lack of access to protect the private resource. To evaluate these obstacles, we develop a spatial-dynamic model of the optimal control of emerald ash borer (EAB) in the Twin Cities metropolitan area of Minnesota, USA. We focus on managing valuable host trees with preventative insecticide treatment or pre-emptive removal to slow EAB spread. The model includes spatial variation in the ownership and benefits of host trees, the costs of management, and the budgets of municipal jurisdictions. We develop and evaluate centralized strategies for 17 jurisdictions surrounding the infestation. The central planner determines the quantities of trees in public ownership to treat and remove over time, to maximize benefits of surviving trees net costs of management across public and private ownerships, subject to constraints on municipal budgets, management activities, and access to private trees. The results suggest that centralizing the budget across jurisdictions rather than increasing any one municipal budget does more to increase total net benefits. Strategies with insecticide treatment are superior to ones with pre-emptive removal because they reduce the quantity of susceptible trees at lower cost and protect the benefits of healthy trees. Increasing the accessibility of private trees to public management substantially slows EAB spread and improves total net benefit. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Invasive species Management Spatial control Emerald ash borer non-linear programming

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The computation of the air conditioning loads life loss and its application to demand response

IET ENERGY SYSTEMS INTEGRATION

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IET ENERGY SYSTEMS INTEGRATION 2024年第3期6卷 242-252页

作者： Li, Zhiwei Hu, Wenhao Cong, Zhihan Zhao, Shuqiang North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewable Baoding Peoples R China

Air conditioning loads (ACLs) represent an increasing proportion of power system loads, offering significant potential for optimised scheduling and active participation in demand response (DR) programs. While many studies have focused on ON/OFF control schemes that satisfy system requirements, few have addressed quantifying the life loss of ACLs from the user perspective. To address this gap, a quantitative model of ACL life loss is established and an optimal scheduling model is developed for ACLs participating in DR that incorporates the cost of life loss. The relationship between life loss and refrigeration power is a complex non-linear high-order fractional function that cannot be solved by commercial solvers. Therefore, a bi-objective multi-weight optimisation algorithm is proposed with a complex non-linear fraction based on the Dinkelbach algorithm and its feasibility through mathematical examples is verified. Finally, a numerical example based on the IEEE 39-bus test system is provided to demonstrate the feasibility of the model and the effectiveness of the proposed solution method.

关键词： distributed power generation mathematical programming non-linear programming optimisation power generation scheduling

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An Optimal Energy Management of Grid-Connected Residential Photovoltaic-Wind-Battery System Under Step-rate and Time-of-Use Tariffs

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INTERNATIONAL JOURNAL OF RENEWABLE ENERGY RESEARCH 2020年第4期10卷 1829-1843页

作者： Azaroual, Meryeme Ouassaid, Mohammed Maaroufi, Mohamed Mohammed V Univ Rabat Engn Smart & Sustainable Syst Res Ctr Mohammadia Sch Engineers EMI Rabat Morocco

This paper explores optimization for energy management for a given residential application. The study proposes an approach that can minimize the utilization of the grid for electricity usage in the load and maximize the sale from renewable energy (photovoltaic (PV) and wind turbine (WT)). Besides, the battery storage is permitted to sell the excess power during high price period. A time-of-use (ToU) and step-rate tariffs are incorporated in the model to control the efficiency of the utility grid and also to consider the fluctuation of the electricity price. Therefore, two energy management methodologies are developed to adjust the tariffs for great benefits. Various residential feed-in tariffs (FIT) are implemented in order to reach the potential of cost-saving and earn more cost-benefit. A typical Moroccan house, containing a grid-connected PV-WT-Battery system, is used for study validation. On the one hand, simulation results show that the developed energy management strategies are effective in controlling the power sources optimally. On the other hand, applying the method under a greater FIT, a lesser requirement of battery capacity will be performed as well as a maximum cost saving. Then, the model as a non-linear Problem (NLP) is compared with another existing optimization approach to ascertain the effectiveness and validity of the algorithm.

关键词： Optimal energy management time-of-use tariff step-rate tariff feed-in tariff non-linear programming Genetic Algorithm

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GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A non-MONOTONE LINE SEARCH TECHNIQUE

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Acta Mathematica Scientia 2005年第1期25卷 170-178页

作者：孙清滢 Department of Applied Mathematics University of Petroleum Dongying 257061 China Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

关键词： non-linear programming three term memory gradient method convergence non-monotone line search technique numerical experiment

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Advertising decisions for a segmented market

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OPTIMIZATION 2009年第4期58卷 469-477页

作者： Viscolani, B. Dept Pure & Appl Math Padua Italy

We consider the problem of choosing the levels of a set of advertising media in order to maximize the firm profit when the market is heterogeneous. Advertising efforts affect the demand of the different segments variably and we assume that the advertising effects on demand over time are mediated by a vector goodwill variable. A first general advertising decision problem is stated and solved in the non-linear programming framework. A preference index is then obtained for the medium selection problem when each segment demand function is linear in goodwill and each medium advertising cost function is quadratic in its level. Finally the theoretical case of disjoint advertising media is discussed.

关键词： advertising market segmentation non-linear programming

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An aggregate constraint method for inequality-constrained least squares problems

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JOURNAL OF GEODESY 2006年第12期79卷 705-713页

作者： Peng, JH Guo, CX Zhang, HP Shong, SL Chongqing Univ Sch Civil Engn Chongqing 400045 Peoples R China Chinese Acad Sci Shanghai Astron Observ Shanghai 200030 Peoples R China State Bur Surveying & Mapping Geodet Data Proc Ctr Xian 710054 Peoples R China Guangdong Univ technol Fac Construct Guangzhou Guangdong Peoples R China

The inequality-constrained least squares (ICLS) problem can be solved by the simplex algorithm of quadratic programming. The ICLS problem may also be reformulated as a Bayesian problem and solved by using the Bayesian principle. This paper proposes using the aggregate constraint method of non-linear programming to solve the ICLS problem by converting many inequality constraints into one equality constraint, which is a basic augmented Lagrangean algorithm for deriving the solution to equality-constrained non-linear programming problems. Since the new approach finds the active constraints, we can derive the approximate algorithm-dependent statistical properties of the solution. As a result, some conclusions about the superiority of the estimator can be approximately made. Two simulated examples are given to show how to compute the approximate statistical properties and to show that the reasonable inequality constraints can improve the results of geodetic network with an ill-conditioned normal matrix.

关键词： inequality-constrained least squares Bayesian estimation minimax estimation non-linear programming aggregate constraint method

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QUANTAL RELEASE OF NEUROTRANSMITTER - AN ITERATIVE METHOD FOR THE AUTOMATIC COMPUTATION OF BINOMIAL-DISTRIBUTION PARAMETERS

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JOURNAL OF NEUROSCIENCE METHODS 1984年第1期10卷 41-50页

作者： BELLUZZI, O UNIV FERRARA INST GEN PHYSIOL I-44100 FERRARA ITALY

A computational method is presented by which, when the amplitude-frequency histogram of the excitatory post-synaptic potentials shows a binomial distribution, an accurate evaluation of the statistical parameters p and n may be obtained. The entire procedure is a combination of 3 basic methods: steepset descent, parabol interpolation and Montecarlo technique. The 2 statistical parameters are evaluated independently with respect to each other, which makes an effective control of the accuracy of the calculation possible by comparing the p by n product with the average number of quanta released in response to each nerve impulse, conventionally computed. Applications to quantal release studies in both rat and guinea pig superior cervical ganglia are also presented.

关键词： quantal release binomial distribution non-linear programming unconstrained minimization

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