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  2. Constrained optimization - Wikipedia

    en.wikipedia.org/wiki/Constrained_optimization

    If the constrained problem has only equality constraints, the method of Lagrange multipliers can be used to convert it into an unconstrained problem whose number of variables is the original number of variables plus the original number of equality constraints. Alternatively, if the constraints are all equality constraints and are all linear ...

  3. Sequential quadratic programming - Wikipedia

    en.wikipedia.org/wiki/Sequential_quadratic...

    Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization which may be considered a quasi-Newton method.SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable, but not necessarily convex.

  4. Unit commitment problem in electrical power production

    en.wikipedia.org/wiki/Unit_Commitment_Problem_in...

    In a free-market regime, the aim is rather to maximize energy production profits, i.e., the difference between revenues (due to selling energy) and costs (due to producing it). If the GenCo is a price maker , i.e., it has sufficient size to influence market prices, it may in principle perform strategic bidding [ 12 ] in order to improve its ...

  5. Optimization problem - Wikipedia

    en.wikipedia.org/wiki/Optimization_problem

    In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions.. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete:

  6. Constraint learning - Wikipedia

    en.wikipedia.org/wiki/Constraint_learning

    The efficiency gain of constraint learning is balanced between two factors. On one hand, the more often a recorded constraint is violated, the more often backtracking avoids doing useless searching. Small inconsistent subsets of the current partial solution are usually better than large ones, as they correspond to constraints that are easier to ...

  7. Nonlinear programming - Wikipedia

    en.wikipedia.org/wiki/Nonlinear_programming

    In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function.

  8. Lagrange multiplier - Wikipedia

    en.wikipedia.org/wiki/Lagrange_multiplier

    The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied. The relationship between the gradient of the function and gradients of the constraints rather naturally leads to a reformulation of the original problem, known as the Lagrangian function or Lagrangian. [2]

  9. Self-supervised learning - Wikipedia

    en.wikipedia.org/wiki/Self-supervised_learning

    The training process involves presenting the model with input data and requiring it to reconstruct the same data as closely as possible. The loss function used during training typically penalizes the difference between the original input and the reconstructed output (e.g. mean squared error).