A Decomposition method for solving quadratic programming (QP) with boxconstraints is presented in this paper. It is similar to the iterative method forsolving linear system of equations. The main ideas of the algorith...
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A Decomposition method for solving quadratic programming (QP) with boxconstraints is presented in this paper. It is similar to the iterative method forsolving linear system of equations. The main ideas of the algorithm are to splitthe Hessian matrix Q of the oP problem into the sum of two matrices N and Hsuch that Q = N + H and (N - H) is symmetric positive definite matrix ((N, H)is called a regular splitting of Q)[5]. A new quadratic programming problem withHessian matrix N to replace the original Q is easier to solve than the originalproblem in each iteration. The convergence of the algorithm is proved under certainassumptions, and the sequence generated by the algorithm converges to optimalsolution and has a linear rate of R-convergence if the matrix Q is positive definite,or a stationary point for the general indefinite matrix Q, and the numerical resultsare also given.
Parallel multisplitting nonlinear iterative methods are established for the system of nonlinear algebraic equations Aψ (x)+Tψ(x) = b, with A, T L(Rn) beingmatrices of particular properties, : Rn→ Rn being diagonal ...
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Parallel multisplitting nonlinear iterative methods are established for the system of nonlinear algebraic equations Aψ (x)+Tψ(x) = b, with A, T L(Rn) beingmatrices of particular properties, : Rn→ Rn being diagonal and continuousmappings, and b ∈ Rn a known vector; and their global convergence are investigated in detail under weaker conditions. Some numerical computations show thatthe new methods have better convergence properties than the known ones in theliterature.
In this paper, based on the mixed variational formulation in [9], a dual mixedvariational formulation for contact problem in elasticity is presented. The existence and uniqueness of the solution of the dual variationa...
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In this paper, based on the mixed variational formulation in [9], a dual mixedvariational formulation for contact problem in elasticity is presented. The existence and uniqueness of the solution of the dual variational problem are discussed,and the error bound O(he3/4) is obtained for Raviart-Thomas (k = 1) elementapproximation.
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