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Integer programming is NP-complete. In particular, the special case of 0–1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems. [1] If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. [2]
A popular algebraic modeling language for linear, mixed-integer and nonlinear optimization. Student and AMPL for courses versions are available for free. APMonitor: Fortran, C++, Python, Matlab, Julia 0.6.2 / March 2016 Yes Yes Dual (Commercial, academic) A differential and algebraic modeling language for mixed-integer and nonlinear optimization.
Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. Bellman explains the reasoning behind the term dynamic programming in his autobiography, Eye of the Hurricane: An Autobiography: I spent the Fall quarter (of 1950) at RAND ...
integer programming constraint programming These branches are all closely intertwined however, since many combinatorial optimization problems can be modeled as integer programs (e.g. shortest path ) or constraint programs, any constraint program can be formulated as an integer program and vice versa, and constraint and integer programs can ...
Branch and price is a branch and bound method in which at each node of the search tree, columns may be added to the linear programming relaxation (LP relaxation). At the start of the algorithm, sets of columns are excluded from the LP relaxation in order to reduce the computational and memory requirements and then columns are added back to the LP relaxation as needed.
solver for mixed integer programming (MIP) and mixed integer nonlinear programming (MINLP). SciPy: BSD general numeric package for Python, with some support for optimization. Uno: MIT Lagrange-Newton solver that unifies nonconvex optimization, implemented in C++. Developed at Argonne National Laboratory and Zuse Institute Berlin. [3]
If integer variables are present, then the problem is referred to as (multi)parametric mixed-integer programming problem [4] If constraints are affine, then additional classifications depending to nature of the objective function in (multi)parametric (mixed-integer) linear, quadratic and nonlinear programming problems is performed. Note that ...
Dynamic programming is both a mathematical optimization method and a computer programming method. It refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart ...