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  2. Mathematical optimization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_optimization

    The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as the special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal.

  3. Multi-objective optimization - Wikipedia

    en.wikipedia.org/wiki/Multi-objective_optimization

    Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.

  4. Dual linear program - Wikipedia

    en.wikipedia.org/wiki/Dual_linear_program

    The weak duality theorem states that the objective value of the dual LP at any feasible solution is always a bound on the objective of the primal LP at any feasible solution (upper or lower bound, depending on whether it is a maximization or minimization problem). In fact, this bounding property holds for the optimal values of the dual and ...

  5. Hamiltonian (control theory) - Wikipedia

    en.wikipedia.org/wiki/Hamiltonian_(control_theory)

    The problem of optimal control is to choose () (from some set ) so that () maximizes or minimizes a certain objective function between an initial time = and a terminal time = (where may be infinity). Specifically, the goal is to optimize over a performance index I ( x ( t ) , u ( t ) , t ) {\displaystyle I(\mathbf {x} (t),\mathbf {u} (t),t ...

  6. Constrained optimization - Wikipedia

    en.wikipedia.org/wiki/Constrained_optimization

    After the problem on variables +, …, is solved, its optimal cost can be used as an upper bound while solving the other problems, In particular, the cost estimate of a solution having x i + 1 , … , x n {\displaystyle x_{i+1},\ldots ,x_{n}} as unassigned variables is added to the cost that derives from the evaluated variables.

  7. Linear least squares - Wikipedia

    en.wikipedia.org/wiki/Linear_least_squares

    Optimal instruments regression is an extension of classical IV regression to the situation where E[ε i | z i] = 0. Total least squares (TLS) [6] is an approach to least squares estimation of the linear regression model that treats the covariates and response variable in a more geometrically symmetric manner than OLS. It is one approach to ...

  8. Value function - Wikipedia

    en.wikipedia.org/wiki/Value_function

    The value function of an optimization problem gives the value attained by the objective function at a solution, while only depending on the parameters of the problem. [1] [2] In a controlled dynamical system, the value function represents the optimal payoff of the system over the interval [t, t 1] when started at the time-t state variable x(t)=x. [3]

  9. Optimization problem - Wikipedia

    en.wikipedia.org/wiki/Optimization_problem

    f : ℝ n → ℝ is the objective function to be minimized over the n-variable vector x, g i (x) ≤ 0 are called inequality constraints; h j (x) = 0 are called equality constraints, and; m ≥ 0 and p ≥ 0. If m = p = 0, the problem is an unconstrained optimization problem. By convention, the standard form defines a minimization problem.