线性规划优化和梯度下降优化之间有什么区别? [英] What is the Difference between Linear programming optimization and a gradient descent optimization?

问题描述

在线性规划问题中，我们制定了两个线性函数和一个优化函数.在其中找到两个线性函数相交的点，并将这些值替换为优化函数中的最大值或最小值.

In linear programming problem we formulate two linear functions and an optimization function. where we find points where the two linear functions intersect and substitute these values in the optimization function to get the max or min.

这与梯度体面优化有何不同?任何人都可以在数学上对此进行详细说明.两种方法都达到全局最大值或最小值吗?哪个更好?

How is this different from a gradient decent optimization. Can anybody elaborate on this mathematically. Are both methods reaching the global maximum or minimum? which is better?

推荐答案

• 线性编程可以找到优化该线性组合的权重.保证有效，但只适用线性组合函数
只要您知道
• 梯度下降的派生类，它就可以对任何函数起作用.但是，只有在函数为凸函数的情况下，才能保证工作.否则它将陷入局部最优状态
• linear programming finds the weights that optimize that linear combination. it is guaranteed to work, but only works for functions that are linear combinations
• gradient descent can work on any function, as long as you know its derivative. However, it is only guaranteed to work if the function is convex. Otherwise it will get stuck at a local optimum

因此，实际上别无选择.如果您有线性组合，则线性编程会更好.在其他所有情况下，梯度下降都是您唯一的选择.

So, there's really no choice. If you have a linear combination, linear programming is better. In every other case, gradient descent is your only option.

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