The main aim of this paper is to generalize the notion of pseudolinearity to nondifferentiable functions and to obtain characterizations for such functions. Under the assumption of pseudolinearity, a characterization ...
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The main aim of this paper is to generalize the notion of pseudolinearity to nondifferentiable functions and to obtain characterizations for such functions. Under the assumption of pseudolinearity, a characterization for the solution sets of an optimization problem and a variational inequality problem has been obtained.
We investigate the optimal partitioning of the end-to-end network QoS budget to quantify the advantage of having a non-uniform allocation of the budget over the links in a path. We formulate an optimization problem th...
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We investigate the optimal partitioning of the end-to-end network QoS budget to quantify the advantage of having a non-uniform allocation of the budget over the links in a path. We formulate an optimization problem that provides a unified framework to study QoS budget allocation. We examine the underlying mathematical structure for the optimal partitioning and dimensioning equations. In the context of network dimensioning, we then show that optimal partitioning can bring large cost reductions as compared with equal partitioning based on the results on small networks. More importantly, we also find that optimal partitioning gives significant improvements in robustness in the presence of failed components and in fairness when the traffic demand is different from the forecast, two effects that had not been observed in previous work and that can have a significant effect on network operations.
A nonlinear programming model for simultaneously coordinated parameters design of power system stabiliser (PSS) and thyristor-based static synchronous compensator (STATCOM) stabiliser is presented. A modified simplex-...
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A nonlinear programming model for simultaneously coordinated parameters design of power system stabiliser (PSS) and thyristor-based static synchronous compensator (STATCOM) stabiliser is presented. A modified simplex-simulated annealing (MSSA) algorithm is developed for solving the programming model. The MSSA can shift all eigenvalues of the system into specified regions on the s-plane for the preconfigured multiple operational points. The MSSA algorithm combines the merits of conventional simplex and simulated annealing methods together, such as global optimal solution, robustness to initial parameter settings and acceptable convergence speed and so on and also improves the ability of solving constrained optimisation problems. Numerical results including eigenvalue analysis and the nonlinear simulation on the 10-generator New England test power system are presented to indicate the effectiveness and potential engineering applications of the MSSA algorithm.
In this paper, we extend the multi-period mean-variance optimization framework to worst-case design with multiple rival return and risk scenarios. Our approach involves a min-max algorithm and a multi-period mean-vari...
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In this paper, we extend the multi-period mean-variance optimization framework to worst-case design with multiple rival return and risk scenarios. Our approach involves a min-max algorithm and a multi-period mean-variance optimization framework for the stochastic aspects of the scenario tree. Multi-period portfolio optimization entails the construction of a scenario tree representing a discretised estimate of uncertainties and associated probabilities in future stages. The expected value of the portfolio return is maximized simultaneously with the minimization of its variance. There are two sources of further uncertainty that might require a strengthening of the robustness of the decision. The first is that some rival uncertainty scenarios may be too critical to consider in terms of probabilities. The second is that the return variance estimate is usually inaccurate and there are different rival estimates, or scenarios. In either case, the best decision has the additional property that, in terms of risk and return, performance is guaranteed in view of all the rival scenarios. The ex-ante performance of min-max models is tested using historical data and backtesting results are presented. (C) 2006 Elsevier B.V. All rights reserved.
A delegated dispatch is a control centre that transmits the requirements of the system operator in critical situations to distributed generation resources, by monitoring and controlling the wind generation producers i...
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A delegated dispatch is a control centre that transmits the requirements of the system operator in critical situations to distributed generation resources, by monitoring and controlling the wind generation producers in a region. When the system needs corrective actions, the system operator sends these requirements to the delegated dispatches. Each delegated dispatch is responsible for matching the goals specified by the system operator, specifying commands and settings to the involved wind generators. In the present paper, some functions of a delegated dispatch are analysed, when applied to a real network. An optimization method is proposed, aiming to reach the regional constraints imposed by the system operator. In the formulation, variations in the output restriction for wind provision, different wind turbines technologies and active and reactive controllability actions are considered. (c) 2006 Elsevier B.V. All rights reserved.
This paper expands previous work dealing with oligopolistic supply chains to the field of closed-loop supply chains. The model presented has been formulated with the intent of examining issues surrounding the recent E...
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This paper expands previous work dealing with oligopolistic supply chains to the field of closed-loop supply chains. The model presented has been formulated with the intent of examining issues surrounding the recent European Union directive regarding waste of electric and electronic equipment (WEEE). The network modelled consists of manufacturers and consumer markets engaged in a Cournot pricing game with perfect information. Closed-loop supply chain network equilibrium occurs when all players agree on volumes shipped and prices charged. Certain properties of the model are examined analytically. Numeric examples are included and have been solved using an extragradient method with constant step size. The equilibrium solution obtained provide interesting insights that lead into a number of areas for future research. (c) 2006 Elsevier B.V. All rights reserved.
This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. More specifically, a modified Hopfield network is developed and its internal parameters are computed usin...
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This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network. (c) 2005 Elsevier Inc. All rights reserved.
We discuss an implementation of a derivative-free generating set search method for linearly constrained minimization with no assumption of nondegeneracy placed on the constraints. The convergence guarantees for genera...
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We discuss an implementation of a derivative-free generating set search method for linearly constrained minimization with no assumption of nondegeneracy placed on the constraints. The convergence guarantees for generating set search methods require that the set of search directions possesses certain geometrical properties that allow it to approximate the feasible region near the current iterate. In the hard case, the calculation of the search directions corresponds to finding the extreme rays of a cone with a degenerate vertex at the origin, a difficult problem. We discuss here how state-of-the-art computational geometry methods make it tractable to solve this problem in connection with generating set search. We also discuss a number of other practical issues of implementation, such as the careful treatment of equality constraints and the desirability of augmenting the set of search directions beyond the theoretically minimal set. We illustrate the behavior of the implementation on several problems from the CUTEr test suite. We have found it to be successful on problems with several hundred variables and linear constraints.
This paper addresses the problem of locating a finite number of sensors to detect an event in a given planar region. The objective is to minimize the maximum probability of non-detection where the underlying region co...
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This paper addresses the problem of locating a finite number of sensors to detect an event in a given planar region. The objective is to minimize the maximum probability of non-detection where the underlying region consists of a convex polygon. The sensor location problem has a multitude of applications, including the location of aircraft detection sensors, the placement of sentries along a border to detect enemy penetration, the detection of nuclear tests, and the detection of natural and hazardous man-made events. The problem is a difficult nonlinear nonconvex programming problem even in the case of two sensors. A fast heuristic based on Voronoi polygons is developed in this paper. The algorithm can quickly generate high-quality solutions. Computational experience is provided. (c) 2006 Elsevier B.V. All rights reserved.
The elastic-mode formulation of the problem of minimizing a nonlinear function subject to equilibrium constraints has appealing local properties in that, for a finite value of the penalty parameter, local solutions sa...
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The elastic-mode formulation of the problem of minimizing a nonlinear function subject to equilibrium constraints has appealing local properties in that, for a finite value of the penalty parameter, local solutions satisfying first- and second-order necessary optimality conditions for the original problem are also first- and second-order points of the elastic-mode formulation. Here we study global convergence properties of methods based on this formulation, which involve generating an (exact or inexact) first- or second-order point of the formulation, for nondecreasing values of the penalty parameter. Under certain regularity conditions on the active constraints, we establish finite or asymptotic convergence to points having a certain stationarity property (such as strong stationarity, M-stationarity, or C-stationarity). Numerical experience with these approaches is discussed. In particular, our analysis and the numerical evidence show that exact complementarity can be achieved finitely even when the elastic-mode formulation is solved inexactly.
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