We consider primal-dual interior point methods where the linear system arising at each iteration is formulated in the reduced (augmented) form and solved approximately. Focusing on the iterates close to a solution, we...
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We consider primal-dual interior point methods where the linear system arising at each iteration is formulated in the reduced (augmented) form and solved approximately. Focusing on the iterates close to a solution, we analyze the accuracy of the so-called inexact step, i.e., the step that solves the unreduced system, when combining the effects of both different levels of accuracy in the inexact computation and different processes for retrieving the step after block elimination. Our analysis is general and includes as special cases sources of inexactness due either to roundoff and computational errors or to the iterative solution of the augmented system using typical procedures. In the roundoff case, we recover and extend some known results.
In the last decade, a new class of interior-exterior algorithms for linear programming was developed. The method was based on the use of mixed penalty function with two separate parameters to solve a set of sub-penali...
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In the last decade, a new class of interior-exterior algorithms for linear programming was developed. The method was based on the use of mixed penalty function with two separate parameters to solve a set of sub-penalized problems associated to the initial problem. To study the necessary optimality conditions, one introduced a new concept of the so-called pseudo-gap to describe fully the optimal primal and dual solutions. Only one Newton iteration is sufficient to approximate the solution of penalized problem which satisfies a criterion of proximity. The purpose of this work is to extend the approach to the convex quadratic programming problems. (c) 2011 IMACS. Published by Elsevier B.V. All rights reserved.
In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the ent...
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In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O（nlog（（ x^0）~TS^0/ε）） which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient.
We propose an exterior Newton method for strictly convex quadratic programming (QP) problems. This method is based on a dual formulation: a sequence of points is generated which monotonically decreases the dual object...
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We propose an exterior Newton method for strictly convex quadratic programming (QP) problems. This method is based on a dual formulation: a sequence of points is generated which monotonically decreases the dual objective function. We show that the generated sequence converges globally and quadratically to the solution (if the QP is feasible and certain nondegeneracy assumptions are satisfied). Measures for detecting infeasibility are provided. The major computation in each iteration is to solve a KKT-like system. Therefore, given an effective symmetric sparse linear solver, the proposed method is suitable for large sparse problems. Preliminary numerical results are reported.
We present a primal interior point method for convex quadratic programming which is based upon a logarithmic barrier function approach. This approach generates a sequence of problems, each of which is approximately so...
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The solution of quadraticprogramming problems is an important issue in the field of mathematical programming and industrial applications. In this paper, we solve convex quadratic programming by a potential-reduction ...
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The solution of quadraticprogramming problems is an important issue in the field of mathematical programming and industrial applications. In this paper, we solve convex quadratic programming by a potential-reduction interior-point algorithm. It is proved that the potential-reduction interior-point algorithm is globally convergent. Some numerical experiments were made.
In this paper, we describe a new primal-dual path-following method to solve a convexquadratic program (QP). The derived algorithm is based on new techniques for finding a new class of search directions similar to the...
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In this paper, we describe a new primal-dual path-following method to solve a convexquadratic program (QP). The derived algorithm is based on new techniques for finding a new class of search directions similar to the ones developed in a recent paper by Darvay for linear programs. We prove that the short-update algorithm finds an epsilon-solution of (QP) in a polynomial time.
This paper presents a pivoting-based method for solving convex quadratic programming and then shows how to use it together with a parameter technique to solve mean-variance portfolio selection problems.
This paper presents a pivoting-based method for solving convex quadratic programming and then shows how to use it together with a parameter technique to solve mean-variance portfolio selection problems.
Using a known result on minimization of convex functionals on polyhedral cones, the Frank-Wolfe theorem, and basic linear algebra, we give a simple proof that the general convex quadratic programming problem which sat...
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Using a known result on minimization of convex functionals on polyhedral cones, the Frank-Wolfe theorem, and basic linear algebra, we give a simple proof that the general convex quadratic programming problem which satisfies a natural necessary condition has a solution.
In this paper we study a form of convexquadratic semi-infinite programming problems with finitely many variables and infinitely many constraints over a compact metric space. An entropic path-following algorithm is in...
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