Given a biobjective linear programming problem,we develop an affine scaling algorithm with min-max direction and demonstrate its convergence for an efficient *** implement the algorithm for some minor issues in the li...
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Given a biobjective linear programming problem,we develop an affine scaling algorithm with min-max direction and demonstrate its convergence for an efficient *** implement the algorithm for some minor issues in the literature.
Analytical models of the actual structure often differ greatly from their as-built counterparts. Model updating techniques improve the predictions of the behavior of the actual structure by identifying and correcting ...
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ISBN:
(纸本)9783037852880
Analytical models of the actual structure often differ greatly from their as-built counterparts. Model updating techniques improve the predictions of the behavior of the actual structure by identifying and correcting the uncertain parameters of the analytical model. This paper presents a new model updating technique to improve the finite element analysis model by updating design parameters using strain measurement based on affinescaling interior algorithm. Static strain measurements are more reliable and realistic than acceleration data in practice. Numerical examples are presented to study the application of the method.
Based on the generalized Dikin-type direction proposed by Jansen et al in 1997, we give out in this paper a generalized Dikin-type affine scaling algorithm for solving the P-*(kappa)-matrix linear complementarity prob...
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Based on the generalized Dikin-type direction proposed by Jansen et al in 1997, we give out in this paper a generalized Dikin-type affine scaling algorithm for solving the P-*(kappa)-matrix linear complementarity problem (LCP). Form using high-order correctors technique and rank-one updating, the iteration complexity and the total computational turn out asymptotically O((kappa + 1)root nL) and O((kappa + 1)n(3)L) respectively.
Mascarenhas gave an instance of linear programming problems to show that the long-step affine scaling algorithm can fail to converge to an optimal solution with the step-size lambda = 0.999. In this note, we give a si...
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Mascarenhas gave an instance of linear programming problems to show that the long-step affine scaling algorithm can fail to converge to an optimal solution with the step-size lambda = 0.999. In this note, we give a simple and clear geometrical explanation for this phenomenon in terms of the Newton barrier flow induced by projecting the homogeneous affinescaling vector field conically onto a hyperplane where the objective function is constant. Based on this interpretation, we show that the algorithm can fail for "any" lambda greater than about 0.91 (a more precise value is 0.91071), which is considerably shorter than lambda = 0.95 and 0.99 recommended for efficient implementations.
In this paper, we introduce an affine scaling algorithm for semidefinite programming (SDP), and give an example of a semidefinite program such that the affine scaling algorithm converges to a non-optimal point. Both o...
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In this paper, we introduce an affine scaling algorithm for semidefinite programming (SDP), and give an example of a semidefinite program such that the affine scaling algorithm converges to a non-optimal point. Both our program and its dual have interior feasible solutions and unique optimal solutions which satisfy strict complementarity, and they are non-degenerate everywhere. (C) 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
In this paper we give a global convergence proof of the second-order affine scaling algorithm for convex quadratic programming problems, where the new iterate is the point which minimizes the objective function over t...
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In this paper we give a global convergence proof of the second-order affine scaling algorithm for convex quadratic programming problems, where the new iterate is the point which minimizes the objective function over the intersection of the feasible region with the ellipsoid centered at the current point and whose radius is a fixed fraction beta is an element of (0;1] of the radius of the largest "scaled" ellipsoid inscribed in the nonnegative orthant. The analysis is based on the local Karmarkar potential function introduced by Tsuchiya. For any beta is an element of (0;1) and without assuming any nondegeneracy assumption on the problem, it is shown that the sequences of primal iterates and dual estimates converge to optimal solutions of the quadratic program and its dual, respectively.
We present two examples in which the dual affine scaling algorithm converges to a vertex that is not optimal if at each iteration we move 0.999 of the step to the boundary of the feasible region.
We present two examples in which the dual affine scaling algorithm converges to a vertex that is not optimal if at each iteration we move 0.999 of the step to the boundary of the feasible region.
We study a trust region affine scaling algorithm for solving the linearly constrained convex or concave programming problem. Under primal nondegeneracy assumption, we prove that every accumulation point of the sequenc...
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We study a trust region affine scaling algorithm for solving the linearly constrained convex or concave programming problem. Under primal nondegeneracy assumption, we prove that every accumulation point of the sequence generated by the algorithm satisfies the first order necessary condition for optimality of the problem. For a special class of convex or concave functions satisfying a certain invariance condition on their Hessians, it is shown that the sequences of iterates and objective function values generated by the algorithm converge R-linearly and e-linearly, respectively. Moreover, under primal nondegeneracy and for this class of objective functions, it is shown that the limit point of the sequence of iterates satisfies the first and second order necessary conditions for optimality of the problem. (C) 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
In this paper we show that a variant of the long-step affine scaling algorithm (with variable stepsizes) is two-step superlinearly convergent when applied to general linear programming (LP) problems, Superlinear conve...
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In this paper we show that a variant of the long-step affine scaling algorithm (with variable stepsizes) is two-step superlinearly convergent when applied to general linear programming (LP) problems, Superlinear convergence of the sequence of dual estimates is also established. For homogeneous LP problems having the origin as the unique optimal solution, we also show that 2/3 is a sharp upper bound on the (fixed) stepsize that provably guarantees that the sequence of primal iterates converge to the optimal solution along a unique direction of approach, Since the point to which the sequence of dual estimates converge depend on the direction of approach of the sequence of primal iterates, this result gives a plausible (but not accurate) theoretical explanation for why 2/3 is a sharp upper bound on the (fixed) stepsize that guarantees the convergence of the dual estimates.
In this paper we present new global convergence results on a long-step affine scaling algorithm obtained by means of the local Karmarkar potential functions. This development was triggered by Dikin's interesting r...
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In this paper we present new global convergence results on a long-step affine scaling algorithm obtained by means of the local Karmarkar potential functions. This development was triggered by Dikin's interesting result on the convergence of the dual estimates associated with a long-step affine scaling algorithm for homogeneous LP problems with unique optimal solutions. Without requiring any assumption on degeneracy, we show that moving a fixed proportion lambda up to two-thirds of the way to the boundary at each iteration ensures convergence of the iterates to an interior point of the optimal face as well as the dual estimates to the analytic center of the dual optimal face, where the asymptotic reduction rate of the value of the objective function is 1-lambda. We also give an example showing that this result is tight to obtain convergence of the dual estimates to the analytic center of the dual optimal face.
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