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1

A Full-Newton Step Interior-point Method Based on a Class of Specific Algebra Transformation

Kheirfam B., Nasrollahi A.

Fundamenta Informaticae

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2018

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Vol. 163, nr 4

325--337

EN

We present a primal-dual path-following interior-point method for linear optimization that is based on the integer powers of the square root function. Our derived search directions is a generalization of the standard directions and the search directions given by Darvay. The proposed algorithm uses only full steps and hence no need to perform line search. We first prove that the iterates lie in the quadratic convergence neighborhood of the proximity measure and then derive the iteration-complexity bound for the algorithm.

2

A Wide Neighborhood Second-order Predictor-corrector Interior-point Algorithm for Semidefinite Optimization with Modified Corrector Directions

Kheirfam B., Mohamadi-Sangachin M.

Fundamenta Informaticae

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2017

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Vol. 153, nr 4

327--346

EN

In this paper, we present a new second-order predictor-corrector interior-point method for semidefinite optimization. The algorithm is based on the wide neighborhood of the central path and modified corrector directions. In the corrector step, we derive the step size and corrector directions which guarantee that new iterate lies in the wide neighborhood. The iteration complexity bound is O(√nlog X0•S0/ɛ) for the Nesterov-Todd direction, which coincides with the best known complexity results for semidefinite optimization. Some numerical results are provided as well.

3

A Predictor-corrector Infeasible-interior-point Algorithm for Semidefinite Optimization in a Wide Neighborhood

Kheirfam B.

Fundamenta Informaticae

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2017

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Vol. 152, nr 1

33--50

EN

In this paper, we propose a predictor-corrector infeasible interior-point algorithm for semidefinite optimization based on the Nesterov-Todd scaling scheme. In each iteration, the algorithm computes the new iterate using a new combination of the predictor and corrector directions. Using the Ai-Zhang's wide neighborhood for linear complementarity problems, and extended to semidefinite optimization by Li and Terlaky, it is shown that the iteration complexity bound of the algorithm is O(n5/4 log ɛ-1 1), where n is the dimension of the problem and ɛ is the required precision.

4

An Arc-search Interior Point Method in the N - ∞ Neighborhood for Symmetric Optimization

Kheirfam B.

Fundamenta Informaticae

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2016

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Vol. 146, nr 3

255--269

EN

In this paper, we propose an arc-search infeasible interior point algorithm for symmetric optimization using the negative infinity neighborhood of the central path. The algorithm searches the optimizers along the ellipses that approximate the entire central path. The convergence of the algorithm is shown for the set of commutative scaling class, which includes some of the most interesting choice of scalings such as xs; sx and the Nesterov-Todd scalings.

5

Postoptimal analysis in the coefficients matrix of piecewise linear fractional programming problems with non-degenerate optimal solution

Kheirfam B.

Opuscula Mathematica

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2010

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Vol. 30, no. 3

281-294

EN

In this paper, we discuss how changes in the coefficients matrix of piecewise linear fractional programming problems affect the non-degenerate optimal solution. We consider separate cases when changes occur in the coefficients of the basic and non-basic variables and derive bounds for each perturbation, while the optimal solution is invariant. We explain that this analysis is a generalization of the sensitivity analysis for LP, LFP and PLP. Finally, the results are described by some numerical examples.

6

Sensitivity analysis in piecewise linear fractional programming problem with non-degenerate optimal solution

Kheirfam B.

Opuscula Mathematica

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2009

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Vol. 29, no. 3

253-269

EN

In this paper, we study how changes in the coefficients of objective function and the right-hand-side vector of constraints of the piecewise linear fractional programming problems affect the non-degenerate optimal solution. We consider separate cases when changes occur in different parts of the problem and derive bounds for each perturbation, while the optimal solution is invariant. We explain that this analysis is a generalization of the sensitivity analysis for LP, LFP and PLP. Finally, the results are described by some numerical examples.