We present a deterministic algorithm that given a tree T with n vertices, a starting vertex v and a slackness parameter ǫ > 0, estimates within an additive error of ǫ the cover and return time, namely, the expected time it takes a simple random walk that starts at v to visit all vertices of T and return to v. The running time of our algorithm is polynomial in n/ǫ, and hence remains polynomial i...

A class of constrained LQ optimal control problems can be abstractly formulated as seeking a nearest point in a `slice' S \ C where S is an aane subspace of a Hilbert space H and C is the (possibly unbounded) closed convex set corresponding to imposition of the constraint. Subject to a slackness condition, it is shown that the optimal control must then be a `nearest point in C' for some control...

A nonlinear optimization problem (P) with inequality constraints can be converted into a new optimization problem (PE) with equality constraints only. This is a Valentine method for finite dimensional optimization. We review second order optimality conditions for (PE) in connection with those of (P). A strictly complementary slackness condition can be made to get the property that sufficient op...

Abstract We propose a simple test for moment inequalities that has exact size in normal models with known variance and uniformly asymptotically under asymptotic normality. The compares the quasi-likelihood ratio statistic to chi-squared critical value, where degree of freedom is rank are active finite samples. requires no simulation thus computationally fast especially suitable constructing con...

The interior trust region algorithm for convex quadratic programming is further developed. This development is motivated by the barrier function and the \center" path-following methods, which create a sequence of primal and dual interior feasible points converging to the optimal solution. At each iteration, the gap between the primal and dual objective values (or the complementary slackness val...

We consider the natural generalizations of blocking and antiblocking polyhedra in infinite dimensions, and study issues related to duality and integrality of extreme points for these sets. Using appropriate finite truncations we give conditions under which complementary slackness holds for primal-dual pairs of the infinite linear programming problems associated with infinite blocking and anti-b...

ABSTRACT This paper provides a short introduction to the Lagrangian duality in convex optimization. At first the topic is motivated by outlining the importance of convex optimization. After that mathematical optimization classes such as convex, linear and non-convex optimization, are defined. Later the Lagrangian duality is introduced. Weak and strong duality are explained and optimality condit...

We have already seen how to take the dual of a linear program in general form. However, when we are solving a problem using linear programming, it can be very enlightening to take the dual of the linear program for that particular problem. Typically, in the context of the problem under study, it is possible to give a natural interpretation to the dual variables, and this also often leads to nat...

assembly line production is one of the widely used basic principles in production system. the problem of assembly line balancing deals with the distribution of activities among the workstations so that there will be maximum utilization of human resources and facilities without disturbing the work sequence. research works reported in the literature mainly deals with minimization of idle time i.e...

The aim of this paper is to establish sufficient local conditions for the uniqueness of solutions to Nonlinear Complementarity Problems (NCP) and Mixed Complementarity Problems (MCP). Our main theorems state that for NCP and MCP defined by continuously differentiable functions, the solution is unique if the Jacobian of the function is a partial P-matrix at each solution. These theorems generali...