On some machine sequencing problems (II)
On stable least squares solution to the system of linear inequalities
The system of inequalities is transformed to the least squares problem on the positive ortant. This problem is solved using orthogonal transformations which are memorized as products. Author’s previous paper presented a method where at each step all the coefficients of the system were transformed. This paper describes a method applicable also to large matrices. Like in revised simplex method, in this method an auxiliary matrix is used for the computations. The algorithm is suitable for unstable...
On the acceleration of adaptation processes by two-step principles
On the Accuracy of Regularized Solutions to Quadratic Minimization Problems on a Half-Space, in Case of a Normally Solvable Operator
On the application of parallel architectures to a class of operations research problems
On the best choice of a damping sequence in iterative optimization methods.
Some iterative methods of mathematical programming use a damping sequence {αt} such that 0 ≤ αt ≤ 1 for all t, αt → 0 as t → ∞, and Σ αt = ∞. For example, αt = 1/(t+1) in Brown's method for solving matrix games. In this paper, for a model class of iterative methods, the convergence rate for any damping sequence {αt} depending only on time t is computed. The computation is used to find the best damping sequence.
On the computer algebra implementation of the least squares method on the nonnegative orthant.
On the convergence of modified relaxation methods for extremum problems
On the convergence rate of empirical estimates in chance constrained stochastic programming
On the convergence rate of regularization methods for ill-posed extremal problems
On the decrease of a quadratic function along the projected-gradient path.
On the degree of asymmetry in the travelling salesman problem
On the efficient update of rectangular LU-factorizations subject to low rank modifications.
On the numerical solution of bound constrained optimization problems
On the numerical solution of optimal control problems with constraints
On the optimum rational function connected with the ADI-method
On the Order of Convergence of Certain Quasi-Newton-Methods.
On the penalty approximation of quadratic programming problem
On the rate of convergence of sequential unconstrained minimization techniques
On the Rate of Superlinear Convergence of a Class of Variable Metric Methods.