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In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the Linear Complementarity Problem. Earlier several authors attempted to propose homotopy functions based on original problems. We propose the homotopy function based on the Karush-Kuhn-Tucker condition of the corresponding quadratic programming problem of the original problem. The proposed approach extends the processability of the larger class of linear complementarity problems and overcomes the limitations of other existing homotopy approaches. We show that the homotopy path approaching the solution is smooth and bounded. We find the positive tangent direction of the homotopy path. The difficulty of finding a strictly feasible initial point for the interior point algorithm can be replaced appropriately by combining the interior point with the homotopy method. Various classes of numerical examples are illustrated to show the effectiveness of the proposed algorithm.
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the solution. The
In this paper, we propose a discretization scheme for the two-stage stochastic linear complementarity problem (LCP) where the underlying random data are continuously distributed. Under some moderate conditions, we derive qualitative and quantitative
The paper is concerned with elongating the shortest curvature-bounded path between two oriented points to an expected length. The elongation of curvature-bounded paths to an expected length is fundamentally important to plan missions for nonholonomic
In this paper, one of our main purposes is to prove the boundedness of solution set of tensor complementarity problem with B tensor such that the specific bounds only depend on the structural properties of tensor. To achieve this purpose, firstly, we
This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate complementa