The primal linear programming problem is defined in canonical form as maxx∈Rds.t.c⊤x,Ax≤b,x≥0.maxx∈Rdc⊤x,s.t.Ax≤b,x≥0. In other words, the objective function and the constraint functions in a linear programming problem are all linear functionals. If we follow the approach a...
Basic Properties Consider the primal semidefinite program where C X = trace CX denotes the inner product of the symmetric matrices C , X ; X Y denotes that the symmetric matrix X Y is positive semidefinite; and : n → R m is a linear operator on the space of symmetric matrices, with ...
A dual for linear programming problems of a two person zero sum constrained matrix game with fuzzy payoffs is introduced and it is proved that such a game is equivalent to a primal-dual pair of certain fuzzy linear programming problems. Itpsilas solution is the focus of discussion in the fut...
Definition:TheDuality in Linear Programmingstates that every linear programming problem has another linear programming problem related to it and thus can be derived from it. The original linear programming problem is called“Primal,”while the derived linear problem is called“Dual.” Before solving fo...
The concept of fuzzy scalar (inner) product that will be used in the fuzzy objective and inequality constraints of the fuzzy primal and dual linear program... Hsien-Chung,Wu - 《Fuzzy Optimization & Decision Making》 被引量: 95发表: 2003年 Duality in infinite dimensional linear programming We...
In 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 the primal is ...
定义1. (Primal and dual problems). 线性规划中,如果原始问题(primal problem)是最小化 ctx 且满足 Ax=b、 x≥0,它的对偶问题(dual problem)是最大化 bty 且满足 Aty≤c (没有关于 y 的限制)。 定理1. 原始问题中的最小值等于对偶问题中的最大值。Brezis 的论文 [3] 提供了一个简洁的证明。 这...
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, ...
A dualproblem is obtained in which multipliers associated with the primal dynamics are pricevectors that are propagated backward in time through a dual dynamical system involvingconditional expectation. A format of Fenchel duality is employed in order to have immediatespecialization not only to linear ...
Primal or dual strong-duality (or min-sup, inf-max duality) in nonconvex optimization is revisited in view of recent literature on the subject, establishing, in particular, new characterizations for the second case. This gives rise to a new class of quasiconvex problems having zero duality gap...