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Behrouz Kheirfam - One of the best experts on this subject based on the ideXlab platform.

  • A wide neighborhood interior-Point Algorithm for linear optimization based on a specific kernel function
    Periodica Mathematica Hungarica, 2019
    Co-Authors: Behrouz Kheirfam, Masoumeh Haghighi
    Abstract:

    This paper presents an interior Point Algorithm for solving linear optimization problems in a wide neighborhood of the central path introduced by Ai and Zhang (SIAM J Optim 16:400–417, 2005). In each iteration, the Algorithm computes the new search directions by using a specific kernel function. The convergence of the Algorithm is shown and it is proved that the Algorithm has the same iteration bound as the best short-step Algorithms. We demonstrate the computational efficiency of the proposed Algorithm by testing some Netlib problems in standard form. To best our knowledge, this is the first wide neighborhood path-following interior-Point method with the same complexity as the best small neighborhood path-following interior-Point methods that uses the kernel function.

  • a full newton step feasible interior Point Algorithm for p κ lcp based on a new search direction
    Croatian Operational Research Review, 2016
    Co-Authors: Behrouz Kheirfam, Masoumeh Haghighi
    Abstract:

    In this paper, we present a full-Newton step feasible interior-Point Algorithm for a  P ∗ ( κ ) linear complementarity problem based on a new search direction. We apply a vector-valued function generated by a univariate function on nonlinear equations of the system which defines the central path. Furthermore, we derive the iteration bound for the Algorithm, which coincides with the best-known iteration bound for these types of Algorithms. Numerical results show that the proposed Algorithm is competitive and reliable.

  • a full nesterov todd step infeasible interior Point Algorithm for symmetric cone linear complementarity problem
    Bulletin of The Iranian Mathematical Society, 2014
    Co-Authors: Behrouz Kheirfam, Nezam Mahdaviamiri
    Abstract:

    A full Nesterov-Todd (NT) step infeasible interior-Point Algorithm is proposed for solving monotone linear complementarity problems over symmetric cones by using Euclidean Jordan algebra. Two types of full NT-steps are used, feasibility steps and centering steps. The Algorithm starts from strictly feasible iterates of a per- turbed problem, and, using the central path and feasibility steps, nds strictly feasible iterates for the next perturbed problem. By using centering steps for the new perturbed problem, strictly fea- sible iterates are obtained to be close enough to the central path of the new perturbed problem. The starting Point depends on two positive numbersp andd. The Algorithm terminates either by nding an ϵ-solution or detecting that the symmetric cone linear complementarity problem has no optimal solution with vanishing duality gap satisfying a condition in terms ofp andd. The it- eration bound coincides with the best known bound for infeasible interior-Point methods. Keywords: Monotone linear complementarity problem, interior- Point Algorithms, Euclidean Jordan algebra. MSC(2010): Primary: 90C33; Secondary: 90C51.

  • a predictor corrector interior Point Algorithm for p κ horizontal linear complementarity problem
    Numerical Algorithms, 2014
    Co-Authors: Behrouz Kheirfam
    Abstract:

    We present a predictor-corrector path-following interior-Point Algorithm for P ? ( ? ) $P_*(\kappa )$ horizontal linear complementarity problem based on new search directions. In each iteration, the Algorithm performs two kinds of steps: a predictor (damped Newton) step and a corrector (full Newton) step. The full Newton-step is generated from an algebraic reformulation of the centering equation, which defines the central path and seeks directions in a small neighborhood of the central path. While the damped Newton step is used to move in the direction of optimal solution and reduce the duality gap. We derive the complexity for the Algorithm, which coincides with the best known iteration bound for P ? ( ? ) $P_*(\kappa )$ -horizontal linear complementarity problems.

  • a full newton step infeasible interior Point Algorithm based on darvay directions for linear optimization
    Journal of Mathematical Modelling and Algorithms, 2014
    Co-Authors: K Ahmadi, F Hasani, Behrouz Kheirfam
    Abstract:

    We present a full-Newton step primal-dual infeasible interior-Point Algorithm based on Darvay’s search directions. These directions are obtained by an equivalent algebraic transformation of the centering equation. The Algorithm decreases the duality gap and the feasibility residuals at the same rate. During this Algorithm we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main iteration of the Algorithm consists of a feasibility step and some centering steps. The starting Point in the first iteration of the Algorithm depends on a positive number ξ and it is strictly feasible for a perturbed pair, and feasibility steps find strictly feasible iterate for the next perturbed pair. By using centering steps for the new perturbed pair, we obtain strictly feasible iterate close to the central path of the new perturbed pair. The Algorithm finds an ϵ-optimal solution or detects infeasibility of the given problem. The iteration bound coincides with the best known iteration bound for linear optimization problems.

F Hasani - One of the best experts on this subject based on the ideXlab platform.

  • a full newton step infeasible interior Point Algorithm based on darvay directions for linear optimization
    Journal of Mathematical Modelling and Algorithms, 2014
    Co-Authors: K Ahmadi, F Hasani, Behrouz Kheirfam
    Abstract:

    We present a full-Newton step primal-dual infeasible interior-Point Algorithm based on Darvay’s search directions. These directions are obtained by an equivalent algebraic transformation of the centering equation. The Algorithm decreases the duality gap and the feasibility residuals at the same rate. During this Algorithm we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main iteration of the Algorithm consists of a feasibility step and some centering steps. The starting Point in the first iteration of the Algorithm depends on a positive number ξ and it is strictly feasible for a perturbed pair, and feasibility steps find strictly feasible iterate for the next perturbed pair. By using centering steps for the new perturbed pair, we obtain strictly feasible iterate close to the central path of the new perturbed pair. The Algorithm finds an ϵ-optimal solution or detects infeasibility of the given problem. The iteration bound coincides with the best known iteration bound for linear optimization problems.

  • a large update feasible interior Point Algorithm for convex quadratic semi definite optimization based on a new kernel function
    Journal of the Operations Research Society of China, 2013
    Co-Authors: Behrouz Kheirfam, F Hasani
    Abstract:

    In this paper we present a large-update primal-dual interior-Point Algorithm for convex quadratic semi-definite optimization problems based on a new parametric kernel function. The goal of this paper is to investigate such a kernel function and show that the Algorithm has the best complexity bound. The complexity bound is shown to be \(\mathcal{O}(\sqrt{n}\log n\log\frac{n}{\epsilon})\).

Yiyuan Tang - One of the best experts on this subject based on the ideXlab platform.

  • letters a fast fixed Point Algorithm for complexity pursuit
    Neurocomputing, 2005
    Co-Authors: Huanwen Tang, Yiyuan Tang
    Abstract:

    Complexity pursuit is a recently developed Algorithm using the gradient descent for separating interesting components from time series. It is an extension of projection pursuit to time series data and the method is closely related to blind separation of time-dependent source signals and independent component analysis (ICA). In this paper, a fixed-Point Algorithm for complexity pursuit is introduced. The fixed-Point Algorithm inherits the advantages of the well-known FastICA Algorithm in ICA, which is very simple, converges fast, and does not need choose any learning step sizes.

  • a new fixed Point Algorithm for independent component analysis
    Neurocomputing, 2004
    Co-Authors: Zhenwei Shi, Huanwen Tang, Yiyuan Tang
    Abstract:

    A new fixed-Point Algorithm for independent component analysis (ICA) is presented that is able blindly to separate mixed signals with sub- and super-Gaussian source distributions. The new fixed-Point Algorithm maximizes the likelihood of the ICA model under the constraint of decorrelation and uses the method of Lee et al. (Neural Comput. 11(2) (1999) 417) to switch between sub- and super-Gaussian regimes. The new fixed-Point Algorithm maximizes the likelihood very fast and reliably. The validity of this Algorithm is confirmed by the simulations and experimental results. (C) 2003 Elsevier B.V. All rights reserved.

H Mansouri - One of the best experts on this subject based on the ideXlab platform.

Lipu Zhang - One of the best experts on this subject based on the ideXlab platform.

  • simplified analysis for full newton step infeasible interior Point Algorithm for semidefinite programming
    Optimization, 2013
    Co-Authors: Lipu Zhang, Liming Sun
    Abstract:

    We present an analysis of the full-Newton step infeasible interior-Point Algorithm for semidefinite optimization, which is an extension of the Algorithm introduced by Roos [C. Roos, A full-Newton step 𝒪(n) infeasible interior-Point Algorithm for linear optimization, SIAM J. Optim. 16 (2006), pp. 1110–1136] for the linear optimization case. We use the proximity measure σ(V) = ‖I − V 2‖ to overcome the difficulty of obtaining an upper bound of updated proximity after one full-Newton step, where I is an identity matrix and V is a symmetric positive definite matrix. It turns out that the complexity analysis of the Algorithm is simplified and the iteration bound obtained is improved slightly.

  • A full-Newton step interior-Point Algorithm based on modified-Newton direction
    Journal of Software, 2011
    Co-Authors: Lipu Zhang
    Abstract:

    By a modification of the classic-Newton direction in scaled version for linear optimization, we give a new interior-Point Algorithm based on a very simple function. The Algorithm uses full modified-Newton step, thus no need to perform line search. In the processing of the Algorithm, the simple function is used to control the searching direction and measure the proximity of iterates to the central path. Moreover, the modified-Newton step used in the Algorithm has local quadratic convergence property according to the proximity function. The iteration complexity is derived, and which is the best-known.

  • a full newton step interior Point Algorithm based on modified newton direction
    Operations Research Letters, 2011
    Co-Authors: Lipu Zhang
    Abstract:

    Abstract The central path plays a very important role in interior-Point methods. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-Point Algorithm based on this search direction, the complexity bound of the Algorithm is the best known for linear optimization.

  • a full newton step interior Point Algorithm for symmetric cone convex quadratic optimization
    Journal of Industrial and Management Optimization, 2011
    Co-Authors: Yanqin Bai, Lipu Zhang
    Abstract:

    In this paper, we present a full-Newton step primal-dual interior-Point Algorithm for solving symmetric cone convex quadratic optimization problem, where the objective function is a convex quadratic function and the feasible set is the intersection of an affine subspace and a symmetric cone lies in Euclidean Jordan algebra. The search directions of the Algorithm are obtained from the modification of NT-search direction in terms of the quadratic representation in Euclidean Jordan algebra. We prove that the Algorithm has a quadratical convergence result. Furthermore, we present the complexity analysis for the Algorithm and obtain the complexity bound as $\left\lceil 2\sqrt{r}\log\frac{\mu^0 r}{\epsilon}\right\rceil$, where $r$ is the rank of Euclidean Jordan algebras where the symmetric cone lies in.

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