On optimal methods in numerical analysis
Round-off error analysis of the gradient method.
On optimizing a maximin nonlinear function subject to replicated quasi-arborescence-like constraints.
In this paper we present the motivation for using the Truncated Newton method in an algorithm that maximises a non-linear function with additional maximin-like arguments subject to a network-like linear system of constraints. The special structure of the network (so-termed replicated quasi-arborescence) allows to introduce the new concept of independent superbasic sets and, then, using second-order information about the objective function without too much computer effort and storage.
On Orthogonal Linear ...1 Approximation.
On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method
For a linear complementarity problem with inconsistent system of constraints a notion of quasi-solution of Tschebyshev type is introduced. It’s shown that this solution can be obtained automatically by Lemke’s method if the constraint matrix of the original problem is copositive plus or belongs to the intersection of matrix classes P 0 and Q 0.
On second–order Taylor expansion of critical values
Studying a critical value function in parametric nonlinear programming, we recall conditions guaranteeing that is a function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of . Several specializations and applications are discussed. These results are understood as supplements to the well–developed theory of first- and second-order directional differentiability of the optimal value function in parametric optimization....
On Solving the Maximum Betweenness Problem Using Genetic Algorithms
In this paper a genetic algorithm (GA) is applied on Maximum Betweennes Problem (MBP). The maximum of the objective function is obtained by finding a permutation which satisfies a maximal number of betweenness constraints. Every permutation considered is genetically coded with an integer representation. Standard operators are used in the GA. Instances in the experimental results are randomly generated. For smaller dimensions, optimal solutions of MBP are obtained by total enumeration. For those...
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