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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. Many algorithms are used to handle the optimization part.
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.
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:
A solver for large scale optimization with API for several languages (C++, java, .net, Matlab and python) TOMLAB: Supports global optimization, integer programming, all types of least squares, linear, quadratic and unconstrained programming for MATLAB. TOMLAB supports solvers like CPLEX, SNOPT and KNITRO. Wolfram Mathematica
A multiple constrained problem could consider both the weight and volume of the books. (Solution: if any number of each book is available, then three yellow books and three grey books; if only the shown books are available, then all except for the green book.) The knapsack problem is the following problem in combinatorial optimization:
Quadratic programming is particularly simple when Q is positive definite and there are only equality constraints; specifically, the solution process is linear. By using Lagrange multipliers and seeking the extremum of the Lagrangian, it may be readily shown that the solution to the equality constrained problem
Constraint satisfaction toolkits are software libraries for imperative programming languages that are used to encode and solve a constraint satisfaction problem. Cassowary constraint solver, an open source project for constraint satisfaction (accessible from C, Java, Python and other languages). Comet, a commercial programming language and toolkit
For each combinatorial optimization problem, there is a corresponding decision problem that asks whether there is a feasible solution for some particular measure m 0. For example, if there is a graph G which contains vertices u and v, an optimization problem might be "find a path from u to v that uses the fewest edges". This problem might have ...