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The constrained-optimization problem (COP) is a significant generalization of the classic constraint-satisfaction problem (CSP) model. [1] COP is a CSP that includes an objective function to be optimized.
A general chance constrained optimization problem can be formulated as follows: (,,) (,,) =, {(,,)}Here, is the objective function, represents the equality constraints, represents the inequality constraints, represents the state variables, represents the control variables, represents the uncertain parameters, and is the confidence level.
Consider the following nonlinear optimization problem in standard form: . minimize () subject to (),() =where is the optimization variable chosen from a convex subset of , is the objective or utility function, (=, …,) are the inequality constraint functions and (=, …,) are the equality constraint functions.
Sequential quadratic programming: A Newton-based method for small-medium scale constrained problems. Some versions can handle large-dimensional problems. Interior point methods: This is a large class of methods for constrained optimization, some of which use only (sub)gradient information and others of which require the evaluation of Hessians.
PDE-constrained optimization is a subset of mathematical optimization where at least one of the constraints may be expressed as a partial differential equation. [1] Typical domains where these problems arise include aerodynamics , computational fluid dynamics , image segmentation , and inverse problems . [ 2 ]
A constraint optimization problem (COP) is a constraint satisfaction problem associated to an objective function. An optimal solution to a minimization (maximization) COP is a solution that minimizes (maximizes) the value of the objective function. During the search of the solutions of a COP, a user can wish for:
In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints .
Constrained optimization. Projected subgradient. One extension of the subgradient method is the projected subgradient method, which solves the constrained ...