A full-Newton step feasible interior-point algorithm for monotone horizontal linear complementarity problems (original) (raw)
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Journal of Applied Mathematics and Computing
This paper contains an infeasible interior-point method for \(P_*(\kappa )\) horizontal linear complementarity problem based on a kernel function. The kernel function is used to determine the search directions. These search directions differ from the usually used ones in some interior-point methods, and their analysis is more complicated. Main feature of our algorithm is that there is no calculation of the step size, i.e, we use full-Newton steps at each iteration. The algorithm constructs strictly feasible iterates for a sequence of perturbations of the given problem, close to its central path. Two types of full-Newton steps are used, feasibility steps and centering steps. The iteration bound matches the best-known iteration bound for these types of algorithms.
Full Newton-Step Interior-Point Method for Linear Complementarity Problems
Croatian Operational Research Review, 2012
In this paper we consider an Infeasible Full Newton-step Interior-Point Method (IFNS-IPM) for monotone Linear Complementarity Problems (LCP). The method does not require a strictly feasible starting point. In addition, the method avoids calculation of the step size and instead takes full Newton-steps at each iteration. Iterates are kept close to the central path by suitable choice of parameters. The algorithm is globally convergent and the iteration bound matches the best known iteration bound for these types of methods.
A Full-Newton Step Interior-Point Method for Monotone Weighted Linear Complementarity Problems
Journal of Optimization Theory and Applications, 2020
In this paper, a full-Newton step Interior-Point Method for solving monotone Weighted Linear Complementarity Problem is designed and analyzed. This problem has been introduced recently as a generalization of the Linear Complementarity Problem with modified complementarity equation, where zero on the right-hand side is replaced with the nonnegative weight vector. With a zero weight vector, the problem reduces to a linear complementarity problem. The importance of Weighted Linear Complementarity Problem lies in the fact that it can be used for modelling a large class of problems from science, engineering and economics. Because the algorithm takes only full-Newton steps, the calculation of the step size is avoided. Under a suitable condition, the algorithm has a quadratic rate of convergence to the target point on the central path. The iteration bound for the algorithm coincides with the best iteration bound obtained for these types of problems.
Improved infeasible-interior-point algorithm for linear complementarity problems
Bulletin of The Iranian Mathematical Society, 2012
We present a modied version of the infeasible-interior- point algorithm for monotone linear complementary problems in- troduced by Mansouri et al. (Nonlinear Anal. Real World Appl. 12(2011) 545{561). Each main step of the algorithm consists of a feasibility step and several centering steps. We use a dierent feasibility step, which targets at the + -center. It results a better iteration bound.
Infeasible penalty interior-point method for linear complementarity problems
International Journal of Informatics and Applied Mathematics, 2022
In this study, we implement a variant of infeasible interiorpoint algorithm for solving monotone linear complementarity problems (LCP). We first reformulate the monotone LCP as an minimization problem. Then a descent iterative method is applied to the latter. The descent direction is computed via the Newton method. However, for maintaining the positivity of iterates, a novel and efficient strategy is proposed. Some numerical results are reported to show the efficiency of our proposed approach.
A polynomial path-following interior point algorithm for general linear complementarity problems
Journal of Global Optimization, 2010
Linear Complementarity Problems (LC Ps) belong to the class of NP-complete problems. Therefore we cannot expect a polynomial time solution method for LC Ps without requiring some special property of the coefficient matrix. Our aim is to construct interior point algorithms which, according to the duality theorem in EP (Existentially Polynomialtime) form, in polynomial time either give a solution of the original problem or detects the lack of property P * (κ), with arbitrary large, but apriori fixedκ). In the latter case, the algorithms give a polynomial size certificate depending on parameterκ, the initial interior point and the input size of the LC P). We give the general idea of an EP-modification of interior point algorithms and adapt this modification to long-step path-following interior point algorithms.