On the behaviour of learning algorithms in a changing environment with application to data network routing problem
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 calculation of steady-state loss probabilities in the queue.
On the central path for nonlinear semidefinite programming
On the central path for nonlinear semidefinite programming
In this paper we study the well definedness of the central path associated to a given nonlinear (convex) semidefinite programming problem. Under standard assumptions, we establish that the existence of the central path is equivalent to the nonemptiness and boundedness of the optimal set. Other equivalent conditions are given, such as the existence of a strictly dual feasible point or the existence of a single central point.The monotonic behavior of the logarithmic barrier and the objective function...
On the central paths and Cauchy trajectories in semidefinite programming
In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a particular case of convex programming with conic constraints. The studied class of functions consists of spectrally defined functions induced by penalty or barrier...
On the characterization of some families of closed convex sets.
On the closure of the sum of closed subspaces.
On the coefficients of the max-algebraic characteristic polynomial and equation
No polynomial algorithms are known for finding the coefficients of the characteristic polynomial and characteristic equation of a matrix in max- algebra. The following are proved: (1) The task of finding the max-algebraic characteristic polynomial for permutation matrices encoded using the lengths of their constituent cycles is NP-complete. (2) The task of finding the lowest order finite term of the max-algebraic characteristic polynomial for a matrix can be converted to the assignment problem....
On the coefficients of variation of uptime and downtime in manufacturing equipment.
On the compatibility of classical multiplier estimates with variable reduction techniques when there are nonlinear inequality constraints.
The minimization of a nonlinear function subject to linear and nonlinear equality constraints and simple bounds can be performed through minimizing a partial augmented Lagrangian function subject only to linear constraints and simple bounds by variable reduction techniques. The first-order procedure for estimating the multiplier of the nonlinear equality constraints through the Kuhn-Tucker conditions is analyzed and compared to that of Hestenes-Powell. There is a method which identifies those major...
On the complexities of selected satisfiability and equivalence queries over Boolean formulas and inclusion queries over hulls.
On the complexity of determining tolerances for ε-optimal solutions to min-max combinatorial optimization problems
This paper studies the complexity of sensitivity analysis for optimal and ε-optimal solutions to general 0-1 combinatorial optimization problems with min-max objectives. Van Hoesel and Wagelmans [9] have studied the complexity of sensitivity analysis of optimal and ε-optimal solutions to min-sum problems, and Ramaswamy et al. [17] the complexity of sensitivity analysis of optimal solutions to min-max problems. We show that under some mild assumptions the sensitivity analysis of ε-optimal solutions...
On the complexity of -player Hackenbush.
On the Complexity of Polyhedral Separability.
On the complexity of the subgraph problem
On the computational complexity of centers locating in a graph
It is shown that the problem of finding a minimum -basis, the -center problem, and the -median problem are -complete even in the case of such communication networks as planar graphs with maximum degree 3. Moreover, a near optimal -center problem is also -complete.
On the computer algebra implementation of the least squares method on the nonnegative orthant.
On the connection between the theory of signal flow graphs and the theory of directed graphs
On the connectivity of efficient point sets
The connectivity of the efficient point set and of some proper efficient point sets in locally convex spaces is investigated.