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Types of Optimization Problems
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Integer Programming (IP)
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.
Stochastic Programming
Optimization involving uncertainty in the data. It accounts for randomness in the constraints or objective function, often through scenarios or probability distributions.
Quadratic Programming (QP)
Optimization where the objective function is quadratic and constraints are linear. It is a special type of nonlinear programming.
Constrained Optimization
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.
Linear Programming (LP)
A mathematical method for determining a way to achieve the best outcome in a given mathematical model. Its functions and constraints are linear.
Multi-objective Optimization
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.
Nonlinear Programming (NLP)
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.
Dynamic Programming (DP)
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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