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Dynamic programming is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics .
Dynamic programming language. In computer science, a dynamic programming language is a class of high-level programming languages which at runtime execute many common programming behaviours that static programming languages perform during compilation. These behaviors could include an extension of the program, by adding new code, by extending ...
Bellman flow chart. A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. [ 1] It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the ...
The Held–Karp algorithm, also called the Bellman–Held–Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman and by Held and Karp to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour that visits each city exactly once before returning to the ...
From a dynamic programming point of view, Dijkstra's algorithm is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method. [26] [27] [28] In fact, Dijkstra's explanation of the logic behind the algorithm, [29] namely Problem 2.
Differential dynamic programming ( DDP) is an optimal control algorithm of the trajectory optimization class. The algorithm was introduced in 1966 by Mayne [1] and subsequently analysed in Jacobson and Mayne's eponymous book. [2] The algorithm uses locally-quadratic models of the dynamics and cost functions, and displays quadratic convergence.
In dynamic programming, a method of mathematical optimization, backward induction is used for solving the Bellman equation. [3] [4] In the related fields of automated planning and scheduling and automated theorem proving, the method is called backward search or backward chaining. In chess, it is called retrograde analysis.
The Needleman–Wunsch algorithm is an algorithm used in bioinformatics to align protein or nucleotide sequences. It was one of the first applications of dynamic programming to compare biological sequences. The algorithm was developed by Saul B. Needleman and Christian D. Wunsch and published in 1970. [ 1] The algorithm essentially divides a ...