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In this paper, we deal with the resolution of the simplicial cone constrained convex quadratic optimization (abbreviated SCQO). It is known that the optimality conditions of SCQO is only a standard linear complementarity problem (LCP). Under a suitable condition, the solution of LCP is equivalent to find the solution of an absolute value equations AVE. For its numerical solution, we propose an efficient two-steps fixed point iterative method for solving the AVE. Moreover, we show that this method converges globally linear to the unique solution of the AVE and which is in turn an optimal solution of SCQO. Some numerical results are reported to demonstrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The aim of this paper is twofold. Firstly, we consider the unique solvability of absolute value equations (AVE), \(Ax-B\vert x\vert =b\), when the condition \(\Vert A^{-1}\Vert

In this paper, we propose a short-step feasible full-Newton step path-following interior-point algorithm (IPA) for monotone linear complementarity problems (LCPs). The proposed IPA uses the technique of algebraic equivalent transformation (AET) induced by an univariate function to transform the centering equations which defines the central-path. By applying Newton's method to the modified system of the central-path of LCP, a new Newton search direction is obtained. Under new appropriate defaults of the threshold τ which defines the size of the neighborhood of the central-path and of θ which determines the decrease in the barrier parameter, we prove that the IPA is well-defined and converges locally quadratically to a solution of the monotone LCPs. Moreover, we derive its iteration bound, namely, O(√nlog n\ϵ) O n log n ε $ \mathcal{O}\left(\sqrt{n}\mathrm{log}\frac{n}{\epsilon }\right)$ which coincides with the best-known iteration bound for such algorithms. Finally, some numerical results are presented to show its efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we deal with unique solvability and numerical solution of absolute value equations (AVE), Ax - B jxj = b, (A,B 2 Rnxn, b 2 Rn). Under some weaker conditions, a simple proof is given for unique solvability of AVE. Furthermore, we demonstrate with an example that these results are reliable to detect unique solvability of AVE. These results are also extended to unique solvability of standard and horizontal linear complementarity problems. Finally, we suggest a Picard iterative method to compute an approximated solution of some uniquely solvable AVE problems where its globally linear convergence is guaranteed via one of our weaker sufficient condition. [ABSTRACT FROM AUTHOR]

In this paper, we consider an optimization model for solving the nonmonotone affine variational inequalities problem (AVI). It is formulated as a DC (Difference of Convex functions) program for which DCA (DC Algorithms) are applied. The resulting DCA are simple: it consists of solving successive convex quadratic program. Numerical experiments on several test problems illustrate the efficiency of the proposed approach in terms of the quality of the obtained solutions and the speed of convergence. [ABSTRACT FROM AUTHOR]

In this paper, a weighted short-step primal-dual path-following interior-point algorithm for solving linear optimization (LO) is presented. The algorithm uses at each interior-point iteration a full-Newton step, thus no need to use line search, and the strategy of the central-path to obtain an 𝜖 -approximated solution of LO. We show that the algorithm yields the iteration bound, namely, 𝒪 (n log n 𝜖). This bound is currently the best iteration bound for LO. Finally, some numerical results are reported in order to analyze the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a feasible primal-dual path-following algorithm for convex quadratic programs. At each interior-point iteration the algorithm uses a full-Newton step and a suitable proximity measure for tracing approximately the central path. We show that the short-step algorithm has the best known iteration bound, namely O(-Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed). [ABSTRACT FROM AUTHOR]