The duality theorem of linear programming is shown to be geometrically and algebraically intuitive when the vertex at which the optimal occurs is simple, i.e. the number of independent hyperplanes intersecting there is exactly the dimension of the space. The result is then extended to the general...
There are several examples in linear algebra and number theory of theorems which are formally similar to the well-known duality theorem of linear programming. The object of this paper is to present a general setting in which we can state and prove a simple criterion for such duality theorems ...
Using an extended version of Choquet's theorem on capacities, an analogue of the classical duality theorem of linear programming is established, imposing only weak conditions on the topology of the spaces Xi and the measurability resp. boundedness of the function h. Applications concern, among ...
摘要: This paper presents a dual of a general linear fractional functionals programming problem. Dual is shown to be a linear programming problem. Along with other duality theorems, complementary slackness theorem is also proved. A simple numerical example illustrates the result....
S.,New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, Vol. 83, No. 1, 1961. Hadley, G.,Nonlinear and Dynamic Programming, Addison-Wesley Publishing Company, Reading, Massachusetts, 1964. Google Scholar Wolfe, P.,A Duality Theorem for Nonlinear Programming, ...
duality theorem Duality, Principle of dual-mode control dual-mode handset dual-mode seeker dual-pitched roof dual-purpose gun Dual-Purpose Reactor dual-rotation engine dual-rotor system dual-scanned liquid-crystal display dual-seal tubing joint ...
We point out a connection between sensitivity analysis and the fundamental theorem of linear programming by characterizing when a linear programming problem has no duality gap. The main result is that the value function is subdifferentiable at the primal constraint if and only if there exists an op...
In addition, an assumption needed to prove the Kuhn-Tucker theorem for the nonlinear problem of Part I is shown in the linear case to be completely analogous to the well-known Slater condition utilized in finite-dimensional programming theory. An example is given that exhibits the essential role...
4.3The duality theorem 4.4Optimal dual variables as marginal costs 4.5Standard form problems and the dual simplex method 4.6Farkas' lemma and linear inequalities 4.7From separating hyperplanes to duality 4.8Cones and extreme rays 4.9Representation of polyhedra 4.10General linear programming duality ...
Many decision situations can be described as multiple objective linear programmes. In this paper, the duality of such programmes is investigated, and the duality theorem is used to illustrate aspects of sensitivity analysis with multiple objectives. Both optimizing and satisficing situations are ...