A security constrained power dispatch problem with non-convex total cost rate function for a lossy electric power system is formulated. Then, an iterative solution method proposed by us and based on modified subgradie...
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A security constrained power dispatch problem with non-convex total cost rate function for a lossy electric power system is formulated. Then, an iterative solution method proposed by us and based on modified subgradient algorithm operating on feasible values (f-msg) is used to solve it. Since all equality and inequality constraints in our nonlinear optimization model are functions of bus voltage magnitudes and phase angles, off-nominal tap settings and susceptance values of svar systems, they are taken as independent variables. Load flow equations are added to the model as equality constraints. The unit generation constraints, transmission line capacity constraints, bus voltage magnitude constraints, off-nominal tap setting constraints and svar system susceptance value constraints are added into the optimization problem as inequality constraints. Since f-msg algorithm requires that all inequality constraints should be expressed in equality constraint form, all inequality constraints are converted into equality constraints by the method, which does not add any extra independent variable into the model and reducing the solution time because of it, before application of it to the optimization model. The proposed technique is tested on IEEE 30-bus and IEEE 57 bus test systems. The minimum total cost rates and the solution times obtained from f-msg algorithm and from the other techniques are compared, and the outperformance of the f-msg algorithm with respect to the other methods in each test system is demonstrated. (C) 2012 Elsevier Ltd. All rights reserved.
In this paper a general mathematical model for portfolio selection problem is proposed. By considering a forecasting performance according to the distributional properties of residuals, we formulate an extended mean-v...
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In this paper a general mathematical model for portfolio selection problem is proposed. By considering a forecasting performance according to the distributional properties of residuals, we formulate an extended mean-variance-skewness model with 11 objective functions. Returns and return errors for each asset obtained using different forecasting techniques, are combined in optimal proportions so as to minimize the mean absolute forecast error. These proportions are then used in constructing six criteria related to the mean, variance and skewness of return forecasts of assets in the future and forecasting errors of returns of assets in the past. The obtained multi-objective model is scalarized by using the conic scalarization method which guarantees to find all non-dominated solutions by considering investor preferences in non-convex multi-objective problems. The obtained scalar problem is solved by utilizing f-msg algorithm. The performance of the proposed approach is tested on a real case problem generated on the data derived from Istanbul Stock Exchange. The comparison is conducted with respect to different levels of investor preferences over return, variance, and skewness and obtained results are summarized. (C) 2010 Elsevier Ltd. All rights reserved.
In this article, we continue to study the modified subgradient (msg) algorithm previously suggested by Gasimov for solving the sharp augmented Lagrangian dual problems. The most important features of this algorithm ar...
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In this article, we continue to study the modified subgradient (msg) algorithm previously suggested by Gasimov for solving the sharp augmented Lagrangian dual problems. The most important features of this algorithm are those that guarantees a global optimum for a wide class of non-convex optimization problems, generates a strictly increasing sequence of dual values, a property which is not shared by the other subgradient methods and guarantees convergence. The main drawbacks ofmsgalgorithm, which are typical for many subgradient algorithms, are those that uses an unconstrained global minimum of the augmented Lagrangian function and requires knowing an approximate upper bound of the initial problem to update stepsize parameters. In this study we introduce a new algorithm based on the so-called feasible values and give convergence theorems. The new algorithm does not require to know the optimal value initially and seeks it iteratively beginning with an arbitrary number. It is not necessary to find a global minimum of the augmented Lagrangian for updating the stepsize parameters in the new algorithm. A collection of test problems are used to demonstrate the performance of the new algorithm.
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