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Solution of Systems of Equalities and Inequalities by the Method of Interior Points

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Abstract

A version of the Newton method is presented. In constructing an auxiliary problem, constraints in the form of inequalities are not considered and the classical extremal problem is solved. Inequalities are taken into account owing to a special choice of weighted coefficients and the step length. Local convergence of the proposed algorithm is studied. The convergence of successive approximations to a relatively interior admissible point of a non-linear system is established.

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REFERENCES

  1. I. I. Dikin, “Investigation of problems of optimal programming by the method of interior points,” in: Optimization Methods, SEI SO Akad. Nauk SSSR, Irkutsk (1975), pp. 72–108.

    Google Scholar 

  2. I. I. Dikin, “Determination of a relatively interior point of a system of constraints in the form of inequalities and equalities,” in: Controlled Systems: Discrete Extremal Problems, 17, IM Akad. Nauk SSSR, Novosibirsk (1978), pp. 60–66.

    Google Scholar 

  3. B. N. Pshenichnyi and Yu. M. Danilin, Numerical Methods in Extremal Problems [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  4. I. I. Dikin, “Convergence of an iterative process,” in: Controlled Systems, 12, IM SO Akad. Nauk SSSR, Novosibirsk (1974), pp. 54–60.

    Google Scholar 

  5. I. I. Dikin and Zorkal'tsev, Iterative Solution of Problems of Mathematical Programming: Algorithms of the Method of Interior Points [in Russian], Nauka, Sib. Otd. RAN, Novosibirsk (1980).

    Google Scholar 

  6. R. J. Vanderbei and J. C. Lagarias, “I. I. Dikin's convergence result for the affine-scaling algorithm,” Contemporary Mathematics, 114, 109–119 (1990).

    Google Scholar 

  7. I. I. Dikin, Determination of Feasible and Optimal Solutions by the Method of Interior Points [in Russian], Nauka, Sib. Otd. RAN, Novosibirsk (1998).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Power Systems, Russian Academy of Sciences, Irkutsk, Russia

    I. I. Dikin

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  1. I. I. Dikin
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Dikin, I.I. Solution of Systems of Equalities and Inequalities by the Method of Interior Points. Cybernetics and Systems Analysis 40, 625–628 (2004). https://doi.org/10.1023/B:CASA.0000047884.38050.0e

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  • DOI: https://doi.org/10.1023/B:CASA.0000047884.38050.0e

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