In this paper, we present a new primal-dual interior-point algorithm for solving a special case of convex quadratic semi-definite optimization based on a parametric kernel function. The proposed parametric kernel func...
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In this paper, we present a new primal-dual interior-point algorithm for solving a special case of convex quadratic semi-definite optimization based on a parametric kernel function. The proposed parametric kernel function is used both for determining the search directions and for measuring the distance between the given iterate and the mu-center for the algorithm. These properties enable us to derive the currently best known iteration bounds for the algorithm with large- and small-update methods, namely, O(root n log n log n/epsilon) and O(root n- log n/epsilon), respectively, which reduce the gap between the practical behavior of the algorithm and its theoretical performance results. (C) 2009 Elsevier Ltd. All rights reserved.
This paper proposes a hybrid machine-learning model, which is called DANN-IP, that combines a deep artificial neural network (DANN) and an interior-point (IP) algorithm in order to improve the prediction capacity on t...
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This paper proposes a hybrid machine-learning model, which is called DANN-IP, that combines a deep artificial neural network (DANN) and an interior-point (IP) algorithm in order to improve the prediction capacity on the patch loading resistance of steel plate girders. For this purpose, 394 steel plate girders that were subjected to patch loading were tested in order to construct the DANN-IP model. Firstly, several DANN models were developed in order to establish the relationship between the patch loading resistance and the web panel length, the web height, the web thickness, the flange width, the flange thickness, the applied load length, the web yield strength, and the flange yield strength of steel plate girders. Accordingly, the best DANN model was chosen based on three performance indices, which included the R(boolean AND)2, RMSE, and a20-index. The IP algorithm was then adopted to optimize the weights and biases of the DANN model in order to establish the hybrid DANN-IP model. The results obtained from the proposed DANN-IP model were compared with of the results from the DANN model and the existing empirical formulas. The comparison showed that the proposed DANN-IP model achieved the best accuracy with an R(boolean AND)2 of 0.996, an RMSE of 23.260 kN, and an a20-index of 0.891. Finally, a Graphical User Interface (GUI) tool was developed in order to effectively use the proposed DANN-IP model for practical applications.
In this paper we propose primal-dual interior-point algorithms for semidefinite optimization problems based on a new kernel function with a trigonometric barrier term. We show that the iteration bounds are for small-u...
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In this paper we propose primal-dual interior-point algorithms for semidefinite optimization problems based on a new kernel function with a trigonometric barrier term. We show that the iteration bounds are for small-update methods and for large-update, respectively. The resulting bound is better than the classical kernel function. For small-update, the iteration complexity is the best known bound for such methods.
We propose a new full-Newton step infeasible interior-point algorithm for monotone linear complementarity problems based on a simple locally-kernel function. The algorithm uses the simple locally-kernel function to de...
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We propose a new full-Newton step infeasible interior-point algorithm for monotone linear complementarity problems based on a simple locally-kernel function. The algorithm uses the simple locally-kernel function to determine the search directions and define the neighborhood of central path. Two types of full-Newton steps are used, feasibility step and centering step. The algorithm starts from strictly feasible iterates of a perturbed problem, on its central path, and feasibility steps find strictly feasible iterates for the next perturbed problem. By using centering steps for the new perturbed problem, we obtain strictly feasible iterates close enough to the central path of the new perturbed problem. The procedure is repeated until an I mu-approximate solution is found. We analyze the algorithm and obtain the complexity bound, which coincides with the best-known result for monotone linear complementarity problems.
In this paper we present a new primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm is based on a new technique for finding the search direction and the strategy of the cent...
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In this paper we present a new primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only full Nesterov-Todd step. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, 0(root n log n/epsilon), which is as good as the linear analogue. (C) 2008 Elsevier Inc. All rights reserved.
Some interior-point algorithms have superlinear convergence. When solving an LCP (linear complementarity problem), superlinear convergence had been achieved under the assumption that a strictly complementary solution ...
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Some interior-point algorithms have superlinear convergence. When solving an LCP (linear complementarity problem), superlinear convergence had been achieved under the assumption that a strictly complementary solution exists, whether starting from a feasible or an infeasible interiorpoint. In this paper, we propose an algorithm for solving monotone geometrical LCPs, and we prove its superlinear convergence without the strictly complementary condition. The algorithm can start from an infeasible interiorpoint and has globally linear convergence. When we use a big initial point or an almost feasible initial point, the algorithm has polynomial time convergence.
This paper proposes a globally convergent predictor-corrector infeasible-interior-point algorithm for the monotone semidefinite linear complementarity problem using the Alizadeh-Haeberly-Overton search direction, and ...
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This paper proposes a globally convergent predictor-corrector infeasible-interior-point algorithm for the monotone semidefinite linear complementarity problem using the Alizadeh-Haeberly-Overton search direction, and shows its quadratic local convergence under the strict complementarity condition.
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 *** goal of this paper is to investigate such a ke...
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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 *** goal of this paper is to investigate such a kernel function and show that the algorithm has the best complexity *** complexity bound is shown to be O(√n log n log n/∈).
As in many primal-dual interior-point algorithms, a primal-dual infeasible-interior-point algorithm chooses a new point along the Newton direction towards a point on the central trajectory, but it does not confine the...
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As in many primal-dual interior-point algorithms, a primal-dual infeasible-interior-point algorithm chooses a new point along the Newton direction towards a point on the central trajectory, but it does not confine the iterates within the feasible region. This paper proposes a step length rule with which the algorithm takes large distinct step lengths in the primal and dual spaces and enjoys the global convergence.
In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and *** algorithm employs a kernel function with a linear growth te...
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In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and *** algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point ***,numerical results illustrate the efficiency of the proposed method.
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