A number of theorems including weak duality theorem, duality theorem, unboundedness theorem, and existence theorem are presented in the chapter to show the relations between the primal and the dual problems. The
linearprogrammingDualityIn this paper, our major theme is a unifying framework for duality in robust linear programming. We show that there are two pair of dual programs allied with a robust linear program; one in which the primal is constructed to be "ultra-conservative" and one in which ...
y≥ c}, and applying weak duality we can use the dual-objective value b T y ∗ as an upper bound for the minimum value being sought. In some cases, we may not need the second step because the primal LP is small with only a few variables. In most cases, however, the LP and it...
定义1. (Primal and dual problems). 线性规划中,如果原始问题(primal problem)是最小化 \mathbf c^t\mathbf x 且满足 \mathbf A\mathbf x=\mathbf b、 \mathbf x\ge\mathbf 0,它的对偶问题(dual problem)是最大化 \mathbf b^t\mathbf y 且满足 \mathbf A^t\mathbf y\leq\mathbf c (没有关于 \...
This discovery re- vealed that every linear programming problem has associated with it another linear pro- gramming problem called the dual. The relationships between the dual problem and the original problem (called the primal) prove to be extremely useful in a variety of ways. For example, ...
In this paper we deal with the minimization of a convex function over the solution set of a range inclusion problem determined by a multivalued operator with convex graph. We attach a dual problem to it, provide regularity conditions guaranteeing strong duality and derive for the resulting primal...
In this paper we consider the duality gap functiongthat measures the difference between the optimal values of the primal problem and of the dual problem in linear programming and in linear semi-infinite programming. We analyze its behavior when the data defining these problems may be perturbed, ...
These duality results are then used to investigate duality for minimax versions of symmetric dual models wherein some of the primal and dual variables are constrained to belong to some arbitrary sets. e.g., the sets of integers.doi:10.1080/02331939808844370...
λ∈Rm (4) Exact ALD for MIPs 5 A well known primal characterization of LD is given by [17] as zLD = inf c x | Ax = b, x ∈ conv(X) . x (5) Remark 2 Note that by rationality of the input data in Assumption 1, zLD is attainable and inf in the objective function of (5...
4) Primal-Dual Linear Programming 原有-对偶线性规划 1. An Application of Homotopy Method to SolvingPrimal-Dual Linear ProgrammingProblems; 应用同伦法求解原有-对偶线性规划问题 5) linear programming problems 线性规划对偶问题 例句>> 6) dual linear programming problem ...