A local acceleration method for primal-dual potential-reduction algorithms is introduced. The method developed here uses modified Newton search directions to minimize the Tanabe-Todd-Ye (TTY) potential function, and can be regarded as a primal-dual variant of the Iri-Imai algorithm based on the multiplicative analogue of Karmarkar's potential function. When iterates are close to an optimal solu...

In this study, an efficient and fast algebraic decoding algorithm (ADA) for the binary systematic quadratic residue (QR) code of length 73 with the reducible generator polynomial to correct up to six errors is proposed. The S(I, J ) matrix method given by He et al. (2001) is utilised to compute the unknown syndromes S5. A technique called swap base is proposed to correct the weight-4 error patt...

We provide a method for efficiently evaluating 2-flip moves that simultaneously change the values of two 0-1 variables in search methods for binary unconstrained quadratic optimization problems (UQP). We extend a framework recently proposed by the authors for creating efficient evaluations of 1-flip moves to yield a method requiring significantly less computation time than a direct sequential a...

In this paper, we seek the conjugate gradient direction closest to the direction of the scaled memoryless BFGS method and propose a family of conjugate gradient methods for unconstrained optimization. An improved Wolfe line search is also proposed, which can avoid a numerical drawback of the Wolfe line search and guarantee the global convergence of the conjugate gradient method under mild condi...

We provide a method for efficiently evaluating two-flip moves that simultaneously change the values of two 0–1 variables in search methods for binary unconstrained quadratic optimisation problems (UQP). We extend a framework recently proposed by the authors for creating efficient evaluations of one-flip moves to yield a method requiring significantly less computation time than a direct sequenti...

We provide a method for efficiently evaluating moves that complement values of 0–1 variables in search methods for binary unconstrained quadratic optimisation problems. Our method exploits a compact matrix representation and offers further improvements in speed by exploiting sparse matrices that arise in large-scale applications. The resulting approach, which works with integer or real data, ca...