Given a linear minimization program, then there is an associated linear maximization program termed the dual. F. E. Clark proved the following theorem. “If the set of feasible points of one program is bounded, then the set of feasible points of the other program is unbounded.” A convex program is the minimization of a convex function subject to the constraint that a number of other convex functions be nonpositive. As is well known, a dual maximization problem can be defined in terms of the Lagrange function. The dual objection function is the infimum of the Lagrange function. The feasible Lagrange multipliers are those satisfying: (i) the multipliers are nonnegative and (ii) the dual objective function is not negative infinity. It is found that Clark's Theorem applies unchanged to dual convex programs. Moreover, the programs have equal values.
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机译：给定一个线性最小化程序，那么就有一个相关的线性最大化程序称为对偶。 F. E. Clark证明了以下定理。 “如果一个程序的可行点集是有界的，那么另一个程序的可行点集是无界的。”凸程序是凸函数的最小化，受其他多个凸函数为非正数的约束。众所周知，可以根据拉格朗日函数来定义对偶最大化问题。双重异议功能是拉格朗日功能的不足。可行的拉格朗日乘数满足以下条件：（i）乘数为非负数；（ii）对偶目标函数不是负无穷大。发现克拉克定理不变地应用于对偶凸程序。此外，程序具有相等的值。
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