The general similarities between dynamic programming and linear programming.

 Dynamic programming and linear programming are two widely used optimization techniques in various fields such as engineering, economics, and operations research. Both techniques aim to find the optimal solution to a problem by maximizing or minimizing an objective function subject to a set of constraints. The objective function in both techniques is linear, and the constraints can also be expressed as linear inequalities or equations.

One of the primary similarities between dynamic programming and linear programming is that they both involve breaking down complex problems into smaller sub-problems that can be solved independently and then combined to find the overall optimal solution. Dynamic programming involves dividing a problem into smaller sub-problems that can be solved recursively, where the solution to a sub-problem is used to solve a larger problem. Similarly, linear programming involves breaking down a problem into smaller sub-problems that can be solved individually and then combined to find the overall optimal solution.

Another similarity between dynamic programming and linear programming is that they both involve evaluating the objective function subject to a set of constraints. In dynamic programming, the objective function is evaluated recursively, while in linear programming, the objective function is evaluated at the corner points of the feasible region.

Finally, both dynamic programming and linear programming require specific assumptions about the problem, such as linearity, additivity, and divisibility, to apply the techniques effectively. Both techniques also require the existence of an optimal solution and a feasible region.

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