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Types of Optimization Problems

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Integer Programming (IP)

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Similar to linear programming, but solutions are required to be integers. It is often used in cases where the variables represent discrete quantities, such as number of items or units.

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Stochastic Programming

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Optimization involving uncertainty in the data. It accounts for randomness in the constraints or objective function, often through scenarios or probability distributions.

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Quadratic Programming (QP)

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Optimization where the objective function is quadratic and constraints are linear. It is a special type of nonlinear programming.

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Constrained Optimization

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Optimization where the solution is subject to equality or inequality constraints. This can encompass LP, NLP, and other kinds of problems, focusing on the presence of limitations on the solution.

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Linear Programming (LP)

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A mathematical method for determining a way to achieve the best outcome in a given mathematical model. Its functions and constraints are linear.

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Multi-objective Optimization

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Deals with optimization problems involving more than one objective function to be optimized simultaneously. Solutions are not single optimal points, but a set of trade-off solutions called Pareto optimal solutions.

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Nonlinear Programming (NLP)

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Concerned with objective functions and/or constraints that are nonlinear. It requires more complex algorithms than LP, such as gradient descent or sequential quadratic programming.

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Dynamic Programming (DP)

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Method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems with a recursive structure and optimal substructure.

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