Over the last four decades Lake Koronia, part of the Mygdonia Basin, operates under a negative water balance due to poor resource management and planning decisions. Lake Koronia is a Ramsar site in northern Greece tha...
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Over the last four decades Lake Koronia, part of the Mygdonia Basin, operates under a negative water balance due to poor resource management and planning decisions. Lake Koronia is a Ramsar site in northern Greece that has experienced pronounced ecosystem degradation over the past 30 years associated with water level reduction and nutrient loading from agricultural and industrial activities. The objective of the present study is the optimal design of an environmental policy for theoretical and potentially in practice return to a sustainable state of the watershed of Lake Koronia and recommend a rational water resource management plan for the area to promote and support development. The use of mathematical modelling tools can assist in making the right decisions with respect to the water management. The increased complexity of simply managing ecosystems, due to many overlapping factors that affect the water balance, impedes the derivation of the optimal policy to address the problems. This paper presents an optimisation model that takes into account all potential investment options that will allow the restoration of the lake and surrounding area to a sustainable level, and determines the optimal operating policy to allow the ecosystem to recover while maintaining the financial stability of the area. Investment options include the transfer of water from larger water sources, creation of irrigation networks and canals, provision of subsidies to promote alternative land use for agriculture and others. The restoration of a sustainable positive water balance for the basin is possible even if future climatic conditions become more arid than the current. Critical aspects are crop manipulation, irrigation networks and a policy to manage water as a commodity rather than an unlimited resource.
In machine learning, regression analysis is a tool for predicting the output variables from a set of known independent variables. Through regression analysis, a function that captures the relationship between the vari...
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In this study, we present a unifying framework for the cones of tangents to an arbitrary set and some of its applications. We highlight the significance of these cones and their polars both from the point of view of d...
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In this study, we present a unifying framework for the cones of tangents to an arbitrary set and some of its applications. We highlight the significance of these cones and their polars both from the point of view of differentiability and subdifferentiability theory and the point of view of mathematical programming. This leads to a generalized definition of a subgradient which extends the well-known definition of a subgradient of a convex function to the nonconvex case. As an application, we develop necessary optimality conditions for a min-max problem and show that these conditions are also sufficient under moderate convexity assumptions.
mathematical programming discriminant analysis models must be normalised to prevent the generation of discriminant functions in which the variable coefficients and the constant term are zero. This normalisation requir...
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mathematical programming discriminant analysis models must be normalised to prevent the generation of discriminant functions in which the variable coefficients and the constant term are zero. This normalisation requirement can cause difficulties, and unlike statistical discriminant analysis, variables cannot be selected in a computationally efficient way with mathematical programming discriminant analysis models. Two new integer programming normalisations are proposed in this paper. In the first, binary variables are used to represent the constant term, but with this normalisation functions with a zero constant term cannot be generated and the variable coefficients are not invariant under origin shifts. These limitations are overcome by using integer programming methods to constrain the sum of the absolute values of the variable coefficients to a constant. These new normalisations are extended to allow variable selection with mathematical programming discriminant analysis models. The use of these new applications of integer programming is illustrated using published data.
The standard decision rules of cost-effectiveness analysis either require the decision maker to set a threshold willingness to pay for additional health care or to set an overall fixed budget. In practice, neither are...
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The standard decision rules of cost-effectiveness analysis either require the decision maker to set a threshold willingness to pay for additional health care or to set an overall fixed budget. In practice, neither are generally taken, but instead an arbitrary decision rule is followed that may not be consistent with the overall budget, lead to an allocation of resources that is less than optimal, and is unable to identify the program that should be displaced at the margin. Recent work has shown how mathematical programming can be used as a generalization of the standard decision rules. The authors extend the use of mathematical programming, first to incorporate more complex budgetary rules about when expenditure can be incurred, and show the opportunity loss, in terms of health benefit forgone, of each budgetary policy. Second, the authors demonstrate that indivisibility in a patient population can be regarded as essentially a concern for horizontal equity and represent this and other equity concerns as constraints in the program. Third, the authors estimate the different opportunity costs of a range of equity concerns applied to particular patient populations, and when imposed on all patient populations. They apply this framework of analysis to a realistic and policy-relevant problem.
Designing compensators with prespecified gain and phase properties has long been a trial-and-error exercise. Some recent efforts to optimize the filter-design process have generated a least-squares fit to some desired...
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Designing compensators with prespecified gain and phase properties has long been a trial-and-error exercise. Some recent efforts to optimize the filter-design process have generated a least-squares fit to some desired filter function. A new technique is presented which optimizes the design process in the L2 sense subject to performance inequality (feasibility) constraints. The achieved filter is shown to be locally optimal as well as feasible. In addition, the developed algorithm can be used to seek a minimal-order optimal filter.
The mathematical notation commonly applied for the formulation of mathematical programming models is extended to include hierarchical structures. The proposed notation is related to hierarchical set concepts in the la...
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The mathematical notation commonly applied for the formulation of mathematical programming models is extended to include hierarchical structures. The proposed notation is related to hierarchical set concepts in the languages UIMP, AMPL, and LPL. With the proposed notation it is possible to aggregate and disaggregate over hierarchical structures. In addition, views are introduced to permit the use of hierarchical substructures and to create new hierarchies out of existing ones. The proposed notation for hierarchical sets and views is illustrated by applying it to the representation and estimation of social accounting matrices (SAMs).
A superstructure-based mathematical model is established for single-contaminant heat-integrated water networks (HIWN), and the water loss of both wastewater regeneration recycling and regeneration reuse is considered....
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A superstructure-based mathematical model is established for single-contaminant heat-integrated water networks (HIWN), and the water loss of both wastewater regeneration recycling and regeneration reuse is considered. Furthermore, a sequential optimization procedure is established to achieve multi-objective optimization. The loss rate of water is taken into the mathematical model as there must have water loss in regeneration process, so that the optimization would be more realistic. Two cases are optimized using proposed model with regeneration recycling and regeneration reuse considered, respectively;the results show the differences between these two modes. Compared with the optimization method in the literature, the proposed method is more realistic.
Typically, exact information of the whole subdifferential is not available for intrinsically nonsmooth objective functions such as for marginal functions. Therefore, the semismoothness of the objective function cannot...
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Typically, exact information of the whole subdifferential is not available for intrinsically nonsmooth objective functions such as for marginal functions. Therefore, the semismoothness of the objective function cannot be proved or is even violated. In particular, in these cases standard nonsmooth methods cannot be used. In this paper, we propose a new approach to develop a converging descent method for this class of nonsmooth functions. This approach is based on continuous outer subdifferentials introduced by us. Further, we introduce on this basis a conceptual optimization algorithm and prove its global convergence. This leads to a constructive approach enabling us to create a converging descentmethod. Within the algorithmic framework, neither semismoothness nor calculation of exact subgradients are required. This is in contrast to other approaches which are usually based on the assumption of semismoothness of the objective function.
This paper presents the problem of fault diagnosis for logically represented continuous systems that can be formulated through nonlinear mathematical programming. This problem is transformed to an integer-programming ...
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This paper presents the problem of fault diagnosis for logically represented continuous systems that can be formulated through nonlinear mathematical programming. This problem is transformed to an integer-programming problem and solved. Possible modifications and extensions of the problem are given. Although failure tables must be prepared in ordinary fault diagnosis, they are not necessary with this mathematical programming approach. By modifying constraints in the mathematical programming problem, difficulties such as multiple faults, correlated faults, modifications of test conditions and cycles in the system, which are encountered in the ordinary failure table approach, are made tractable.
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