• Title/Summary/Keyword: superlinear problems

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POSITIVE SOLUTIONS OF SUPERLINEAR AND SUBLINEAR BOUNDARY VALUE PROBLEMS

  • Gatica, Juan A.;Kim, Yun-Ho
    • Korean Journal of Mathematics
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    • v.25 no.1
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    • pp.37-43
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    • 2017
  • We study the existence of positive solutions of second order nonlinear separated boundary value problems of superlinear as well as sublinear type without imposing monotonicity restrictions on the problem. The type of problem investigated cannot be analyzed using the linearization about the trivial solution because either it does not exist (the sublinear case) or is trivial (the superlinear case). The results follow from a known fixed point theorem by noticing that the concavity of the solutions provides an important condition for the applicability of the fixed point result.

A DUAL ALGORITHM FOR MINIMAX PROBLEMS

  • HE SUXIANG
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.401-418
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    • 2005
  • In this paper, a dual algorithm, based on a smoothing function of Bertsekas (1982), is established for solving unconstrained minimax problems. It is proven that a sequence of points, generated by solving a sequence of unconstrained minimizers of the smoothing function with changing parameter t, converges with Q-superlinear rate to a Kuhn-Thcker point locally under some mild conditions. The relationship between the condition number of the Hessian matrix of the smoothing function and the parameter is studied, which also validates the convergence theory. Finally the numerical results are reported to show the effectiveness of this algorithm.

A SUPERLINEAR $\mathcal{VU}$ SPACE-DECOMPOSITION ALGORITHM FOR SEMI-INFINITE CONSTRAINED PROGRAMMING

  • Huang, Ming;Pang, Li-Ping;Lu, Yuan;Xia, Zun-Quan
    • Journal of applied mathematics & informatics
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    • v.30 no.5_6
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    • pp.759-772
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    • 2012
  • In this paper, semi-infinite constrained programming, a class of constrained nonsmooth optimization problems, are transformed into unconstrained nonsmooth convex programs under the help of exact penalty function. The unconstrained objective function which owns the primal-dual gradient structure has connection with $\mathcal{VU}$-space decomposition. Then a $\mathcal{VU}$-space decomposition method can be applied for solving this unconstrained programs. Finally, the superlinear convergence algorithm is proved under certain assumption.

EXISTENCE OF POSITIVE SOLUTIONS FOR GENERALIZED LAPLACIAN PROBLEMS WITH A PARAMETER

  • Kim, Chan-Gyun
    • East Asian mathematical journal
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    • v.38 no.1
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    • pp.33-41
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    • 2022
  • In this paper, we study singular Dirichlet boundary value problems involving ϕ-Laplacian. Using fixed point index theory, the existence of positive solutions is established under the assumption that the nonlinearity f = f(u) has a positive falling zero and is either superlinear or sublinear at u = 0.

AN ADAPTIVE APPROACH OF CONIC TRUST-REGION METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS

  • FU JINHUA;SUN WENYU;SAMPAIO RAIMUNDO J. B. DE
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.165-177
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    • 2005
  • In this paper, an adaptive trust region method based on the conic model for unconstrained optimization problems is proposed and analyzed. We establish the global and super linear convergence results of the method. Numerical tests are reported that confirm the efficiency of the new method.

BROYDEN'S METHOD FOR OPERATORS WITH REGULARLY CONTINUOUS DIVIDED DIFFERENCES

  • Galperin, Anatoly M.
    • Journal of the Korean Mathematical Society
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    • v.52 no.1
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    • pp.43-65
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    • 2015
  • We present a new convergence analysis of popular Broyden's method in the Banach/Hilbert space setting which is applicable to non-smooth operators. Moreover, we do not assume a priori solvability of the equation under consideration. Nevertheless, without these simplifying assumptions our convergence theorem implies existence of a solution and superlinear convergence of Broyden's iterations. To demonstrate practical merits of Broyden's method, we use it for numerical solution of three nontrivial infinite-dimensional problems.

ANALYSIS OF SMOOTHING NEWTON-TYPE METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS

  • Zheng, Xiuyun
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1511-1523
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    • 2011
  • In this paper, we consider the smoothing Newton method for the nonlinear complementarity problems with $P_0$-function. The proposed algorithm is based on a new smoothing function and it needs only to solve one linear system of equations and perform one line search per iteration. Under the condition that the solution set is nonempty and bounded, the proposed algorithm is proved to be convergent globally. Furthermore, the local superlinearly(quadratic) convergence is established under suitable conditions. Preliminary numerical results show that the proposed algorithm is very promising.