Description:
In this paper we study relations between the directional derivatives, the weak subdifferentials, and the radial epiderivatives for nonconvex real-valued functions. We generalize the well-known theorem that represents the directional derivative of a convex function as a pointwise maximum of its subgradients for the nonconvex case. Using the notion of the weak subgradient, we establish conditions that guarantee equality of the directional derivative to the pointwise supremum of weak subgradients of a nonconvex real-valued function. A similar representation is also established for the radial epiderivative of a nonconvex function. Finally the equality between the directional derivatives and the radial epiderivatives for a nonconvex function is proved. An analogue of the well-known theorem on necessary and sufficient conditions for optimality is drawn without any convexity assumptions.
Description:
In this paper we study relations between the directional derivatives, the weak subdifferentials, and the radial epiderivatives for nonconvex real-valued functions. We generalize the well-known theorem that represents the directional derivative of a convex function as a pointwise maximum of its subgradients for the nonconvex case. Using the notion of the weak subgradient, we establish conditions that guarantee equality of the directional derivative to the pointwise supremum of weak subgradients of a nonconvex real-valued function. A similar representation is also established for the radial epiderivative of a nonconvex function. Finally the equality between the directional derivatives and the radial epiderivatives for a nonconvex function is proved. An analogue of the well-known theorem on necessary and sufficient conditions for optimality is drawn without any convexity assumptions.
Description:
Optimization of multiple classifiers is an important problem in data mining. We introduce additional structure on the class sets of the classifiers using string rewriting systems with a convenient matrix representation. The aim of the present paper is to develop an efficient algorithm for the optimization of the number of errors of individual classifiers, which can be corrected by these multiple classifiers.
Description:
Optimization of multiple classifiers is an important problem in data mining. We introduce additional structure on the class sets of the classifiers using string rewriting systems with a convenient matrix representation. The aim of the present paper is to develop an efficient algorithm for the optimization of the number of errors of individual classifiers, which can be corrected by these multiple classifiers.
Description:
In this paper we consider the problem of finding optimal parameters of the Kelvin element in vibration analysis. This problem is based on finding analytical solution of the initial ODE for development of the optimization model. Such technique allows us to compute optimal parameters of Kelvin element.
Description:
In this paper we consider the problem of finding optimal parameters of the Kelvin element in vibration analysis. This problem is based on finding analytical solution of the initial ODE for development of the optimization model. Such technique allows us to compute optimal parameters of Kelvin element.
Description:
In this paper, a novel learning strategy for radial basis function networks (RBFN) is proposed. By adjusting the parameters of the hidden layer, including the RBF centers and widths, the weights of the output layer are adapted by local optimization methods. A new local optimization algorithm based on a combination of the gradient and Newton methods is introduced. The efficiency of some local optimization methods to Update the weights of RBFN is Studied in solving systems of nonlinear integral equations. (C) 2009 Elsevier Ltd. All rights reserved.
Description:
This article considers the application of the notion of statistical convergence in turnpike theory. The first results have been obtained recently [, , ]. We briefly discuss the importance of this conjunction, present some results obtained and, finally, we formulate a challenge problem for future investigations.
Description:
We consider the problem of solving a constrained system of nonlinear equations. After reformulating the system into an equivalent constrained global optimization problems, we construct a filled function based on a special property of the reformulated problem. A filled function method is then proposed to solve the constrained system of nonlinear equations. Some numerical examples are presented to illustrate the usefulness of the present techniques.
Description:
In this paper, we propose an auxiliary function method to solve constrained systems of nonlinear equations. By introducing an auxiliary function, an unconstrained (box-constrained) optimization problem is constructed for a given constrained system of nonlinear equations. It is shown that any local minimizer of the constructed unconstrained optimization problem is an approximate solution to the given constrained system when parameters are appropriately chosen, and the precision for approximation can be preset. It is also shown that any accumulation point of the local minimizers of the constructed unconstrained optimization problems with a sequence of parameters tending to zero is a solution to the given constrained system of nonlinear equations.
Description:
This study predicts whether it is best to buy, hold or sell shares (trading signals) of the All Share Price Index (ASPI) of the Colombo Stock Exchange, using a modified neural network (NN) algorithm. Most commonly used classification techniques are not successful in predicting trading signals when the distribution of the actual trading signals, among these three classes, is imbalanced. The structure of this modified neural network is same as that of feedforward neural networks. This algorithm minimises a modified Ordinary Least Squares (OLS) error function. An adjustment relating to the contribution from the historical data used for training the networks, and penalisation of incorrectly classified trading signals were accounted for, when modifying the OLS function. A global optimization algorithm was employed to train these networks. Results obtained were satisfactory.
Description:
IIntroducing a new concept of (®, ¯)-fairness, which allows for a bounded fairness compromise, so that a source is allocated a rate neither less than 0 · ® · 1, nor more than ¯ ¸ 1, times its fair share, this paper provides a framework to optimize efficiency (utilization, throughput or revenue) subject to fairness constraints in a general telecommunications network for an arbitrary fairness criterion and cost functions. We formulate a non-linear program (NLP) that finds the optimal bandwidth allocation by maximizing efficiency subject to (®, ¯)-fairness constraints. This leads to what we call an efficiency-fairness function, which shows the benefit in efficiency as a function of the extent to which fairness is compromised. To solve the NLP we use two algorithms. The first is a well known branch-and-bound-based algorithm called Lipschitz Global Optimization and the second is a recently developed algorithm called Algorithm for Global Optimization Problems (AGOP). We demonstrate the applicability of the framework to a range of example from sharing a single link to efficiency fairness issues associated with serving customers in remote communities.
Description:
IIntroducing a new concept of (®, ¯)-fairness, which allows for a bounded fairness compromise, so that a source is allocated a rate neither less than 0 · ® · 1, nor more than ¯ ¸ 1, times its fair share, this paper provides a framework to optimize efficiency (utilization, throughput or revenue) subject to fairness constraints in a general telecommunications network for an arbitrary fairness criterion and cost functions. We formulate a non-linear program (NLP) that finds the optimal bandwidth allocation by maximizing efficiency subject to (®, ¯)-fairness constraints. This leads to what we call an efficiency-fairness function, which shows the benefit in efficiency as a function of the extent to which fairness is compromised. To solve the NLP we use two algorithms. The first is a well known branch-and-bound-based algorithm called Lipschitz Global Optimization and the second is a recently developed algorithm called Algorithm for Global Optimization Problems (AGOP). We demonstrate the applicability of the framework to a range of example from sharing a single link to efficiency fairness issues associated with serving customers in remote communities.
Description:
In this paper, we propose a new global optimization approach based on the filled function method for solving box-constrained systems of nonlinear equations. The special properties of optimization problem are employed to construct a novel filled function. The objective function value can be reduced by half in each iteration of our filled function algorithm. Several numerical examples are presented to illustrate the efficiency of the present approach.