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  2. Constrained optimization - Wikipedia

    en.wikipedia.org/wiki/Constrained_optimization

    Many constrained optimization algorithms can be adapted to the unconstrained case, often via the use of a penalty method.However, search steps taken by the unconstrained method may be unacceptable for the constrained problem, leading to a lack of convergence.

  3. Lagrange multiplier - Wikipedia

    en.wikipedia.org/wiki/Lagrange_multiplier

    For example, in economics the optimal profit to a player is calculated subject to a constrained space of actions, where a Lagrange multiplier is the change in the optimal value of the objective function (profit) due to the relaxation of a given constraint (e.g. through a change in income); in such a context is the marginal cost of the ...

  4. Constrained least squares - Wikipedia

    en.wikipedia.org/wiki/Constrained_least_squares

    In constrained least squares one solves a linear least squares problem with an additional constraint on the solution. [ 1 ] [ 2 ] This means, the unconstrained equation X β = y {\displaystyle \mathbf {X} {\boldsymbol {\beta }}=\mathbf {y} } must be fit as closely as possible (in the least squares sense) while ensuring that some other property ...

  5. Karush–Kuhn–Tucker conditions - Wikipedia

    en.wikipedia.org/wiki/Karush–Kuhn–Tucker...

    For the constrained case, the situation is more complicated, and one can state a variety of (increasingly complicated) "regularity" conditions under which a constrained minimizer also satisfies the KKT conditions. Some common examples for conditions that guarantee this are tabulated in the following, with the LICQ the most frequently used one:

  6. Chance constrained programming - Wikipedia

    en.wikipedia.org/wiki/Chance_constrained_programming

    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.

  7. Constraint (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Constraint_(mathematics)

    Under certain conditions, as for example in convex optimization, if a constraint is non-binding, the optimization problem would have the same solution even in the absence of that constraint. If a constraint is not satisfied at a given point, the point is said to be infeasible .

  8. Quadratically constrained quadratic program - Wikipedia

    en.wikipedia.org/wiki/Quadratically_constrained...

    A commercial optimization solver for linear programming, non-linear programming, mixed integer linear programming, convex quadratic programming, convex quadratically constrained quadratic programming, second-order cone programming and their mixed integer counterparts. AMPL: CPLEX: Popular solver with an API for several programming languages.

  9. Barrier function - Wikipedia

    en.wikipedia.org/wiki/Barrier_function

    Consider the following constrained optimization problem: minimize f(x) subject to x ≤ b. where b is some constant. If one wishes to remove the inequality constraint, the problem can be reformulated as minimize f(x) + c(x), where c(x) = ∞ if x > b, and zero otherwise. This problem is equivalent to the first.