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An Interior Point Potential Reduction Method for Constrained Equations
, 1995
"... We study the problem of solving a constrained system of nonlinear equations by a combination of the classical damped Newton method for (unconstrained) smooth equations and the recent interior point potential reduction methods for linear programs, linear and nonlinear complementarity problems. In gen ..."
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Cited by 11 (3 self)
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We study the problem of solving a constrained system of nonlinear equations by a combination of the classical damped Newton method for (unconstrained) smooth equations and the recent interior point potential reduction methods for linear programs, linear and nonlinear complementarity problems. In general, constrained equations provide a unified formulation for many mathematical programming problems, including complementarity problems of various kinds and the KarushKuhnTucker systems of variational inequalities and nonlinear programs. Combining ideas from the damped Newton and interior point methods, we present an iterative algorithm for solving a constrained system of equations and investigate its convergence properties. Specialization of the algorithm and its convergence analysis to complementarity problems of various kinds and the KarushKuhnTucker systems of variational inequalities are discussed in detail. We also report the computational results of the implementation of the algo...
A Unifying Investigation of InteriorPoint Methods for Convex Programming
 Faculty of Mathematics and Informatics, TU Delft, NL2628 BL
, 1992
"... In the recent past a number of papers were written that present low complexity interiorpoint methods for different classes of convex programs. Goal of this article is to show that the logarithmic barrier function associated with these programs is selfconcordant, and that the analyses of interiorpo ..."
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Cited by 5 (4 self)
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In the recent past a number of papers were written that present low complexity interiorpoint methods for different classes of convex programs. Goal of this article is to show that the logarithmic barrier function associated with these programs is selfconcordant, and that the analyses of interiorpoint methods for these programs can thus be reduced to the analysis of interiorpoint methods with selfconcordant barrier functions. Key words: interiorpoint method, barrier function, dual geometric programming, (extended) entropy programming, primal and dual l p programming, relative Lipschitz condition, scaled Lipschitz condition, selfconcordance. 1 Introduction The efficiency of a barrier method for solving convex programs strongly depends on the properties of the barrier function used. A key property that is sufficient to prove fast convergence for barrier methods is the property of selfconcordance introduced in [17]. This condition not only allows a proof of polynomial convergen...
An Algorithm for Posynomial Geometric Programming, Based on Generalized Linear Programming
, 1995
"... This paper describes a column generation algorithm for posynomial geometric programming that ..."
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This paper describes a column generation algorithm for posynomial geometric programming that
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"... Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are estimating of actual values. This paper develops a solution ..."
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Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are estimating of actual values. This paper develops a solution procedure to solve nonlinear programming problems using GP technique by splitting the cost coefficients, constraint coefficients and exponents with the help of binary numbers. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem. The ability of calculating the cost coefficients, constraint coefficients and exponents developed in this paper might help lead to more realistic modeling efforts in engineering design areas. Standard nonlinear programming software has been used to solve the proposed optimization problem. Two numerical examples are presented to illustrate the method.