Give a set of mean - value theorem in open - interval with non - differentiable points
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Therefor , this chapter puts forward the solution of non - differentiable equations
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Higher order f - convexity and higher order symmetric duality in non - differentiable mathematical programming
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But these methods are designed to solve differen - tiable problems , they will be no use when meeting with non - differentiable equations
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Chapter one : this chapter discuss mainly about the astringency of several deformed newton ' s iterative methods and their application in solution of non - differentiable problems
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The object functions for synthesis of array antennas usually have the characteristics of multi - parameters , non - differentiable even discontinuities . the optimization of pattern function is non - linear problem
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Continuity , integrability and differentiability of riemann function are discussed ; especially , the non - differentiable properties on [ 0 , 1 ] are proved , and dirichlet ' s function is comparated with it
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It can speed the local rate of convergence and improve the accuracy of solution , and to solve nonlinear constraint optimization problems , coa was combined with exact non - differentiable penalty function
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As a powerful global optimization approach , genetic algorithms ( ga ) can solve a variety of optimization problems in which the objective function is discontinuous , non - differentiable , or highly non - linear , to produce high convergence speed and vast search space
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Furthermore , when replacing the entropy function by a general separate multiplier function , we develop a new regularization approach , referred to as lagrangian regularization approach . this approach does not only provide a unified smoothing technique for the non - differentiable m ( x ) and but also offers a unified framework for constructing penalty functions , whereby building a bridge between the penalty functions and the classical lagrangian
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