Balinski and Tucker introduced in 1969 a special form of optimal tableaus for LP, which can be used to construct primal and dual optimal solutions such that the complementary slackness relation holds strictly. In this paper, first we note that using a polynomial time algorithm for LP Balinski and Tucker’s tableaus are obtainable in polynomial time. Furthermore, we show that, given a pair of pri...

Computation of pairs of analysis and synthesis (dual) windows is very important in using discrete-time Gabor transform. Biorthogonal-like sequence theory ooers some simple solutions for computing dual windows for signal representation. Solutions to the biorthogonal-like condition are obtained by dividing the problem into various cases. As an example, dual windows for the truncated Gaussian wind...

We consider Continuous Linear Programs over a continuous finite time horizon T , with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the Separated Continuous Linear Programming models and ...

We provide a characterization of the symmetric and weighted versions of the Euclidean compromise solution for multiobjective optimization problems first proposed by P.L.Yu. These solutions minimize a measure of the distance between a feasible set and the utopia point of that set, and are closely related to solutions that have been proposed in the bargaining with claims literature. We provide ne...

Linear programming (LP)-based relaxations have proven to be useful in enumerative solution procedures for N P-hard min-sum scheduling problems. We take a dual viewpoint of the time-indexed integer linear programming (ILP) formulation for these problems. Previously proposed Lagrangian relaxation methods and a time decomposition method are interpreted and synthesized under this view. Our new resu...

The discovery of self-dual instanton solutions in Euclidean Yang-Mills theory [I] has recently stimulated a great deal of interest in self-dual solutions to Einstein’s theory of gravitation. One would expect that the relevant instanton-like metrics would be those whose gravitational fields are self-dual, localized in Euclidean spacetime and free of singularities. In fact, solutions have been fo...

We study the domain wall soliton solutions in the relativistic self-dual Maxwell Chern-Simons model in 1+1 dimensions obtained by the dimensional reduction of the 2 + 1 model. Both topological and nontopological self-dual solutions are found in this case. A la BPS dyons here the Bogomol’ny bound on the energy is expressed in terms of two conserved quantities. We discuss the underlying supersymm...

This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions...