enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Second-order cone programming - Wikipedia

    en.wikipedia.org/wiki/Second-order_cone_programming

    The "second-order cone" in SOCP arises from the constraints, which are equivalent to requiring the affine function (+, +) to lie in the second-order cone in +. [ 1 ] SOCPs can be solved by interior point methods [ 2 ] and in general, can be solved more efficiently than semidefinite programming (SDP) problems. [ 3 ]

  3. Convex optimization - Wikipedia

    en.wikipedia.org/wiki/Convex_optimization

    In LP, the objective and constraint functions are all linear. Quadratic programming are the next-simplest. In QP, the constraints are all linear, but the objective may be a convex quadratic function. Second order cone programming are more general. Semidefinite programming are more general. Conic optimization are even more general - see figure ...

  4. Conic optimization - Wikipedia

    en.wikipedia.org/wiki/Conic_optimization

    Examples of include the positive orthant + = {:}, positive semidefinite matrices +, and the second-order cone {(,): ‖ ‖}. Often f {\displaystyle f\ } is a linear function, in which case the conic optimization problem reduces to a linear program , a semidefinite program , and a second order cone program , respectively.

  5. Quadratically constrained quadratic program - Wikipedia

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

    To see this, note that the two constraints x 1 (x 11) ≤ 0 and x 1 (x 11) ≥ 0 are equivalent to the constraint x 1 (x 11) = 0, which is in turn equivalent to the constraint x 1 ∈ {0, 1}. Hence, any 0–1 integer program (in which all variables have to be either 0 or 1) can be formulated as a quadratically constrained ...

  6. Bilevel optimization - Wikipedia

    en.wikipedia.org/wiki/Bilevel_optimization

    Bilevel optimization is a special kind of optimization where one problem is embedded (nested) within another. The outer optimization task is commonly referred to as the upper-level optimization task, and the inner optimization task is commonly referred to as the lower-level optimization task.

  7. Constrained optimization - Wikipedia

    en.wikipedia.org/wiki/Constrained_optimization

    Alternatively, if the constraints are all equality constraints and are all linear, they can be solved for some of the variables in terms of the others, and the former can be substituted out of the objective function, leaving an unconstrained problem in a smaller number of variables.

  8. MUSCL scheme - Wikipedia

    en.wikipedia.org/wiki/MUSCL_scheme

    Thus, the accuracy of a TVD discretization degrades to first order at local extrema, but tends to second order over smooth parts of the domain. The algorithm is straight forward to implement. Once a suitable scheme for F i + 1 / 2 ∗ {\displaystyle F_{i+1/2}^{*}} has been chosen, such as the Kurganov and Tadmor scheme (see below), the solution ...

  9. Linear complementarity problem - Wikipedia

    en.wikipedia.org/wiki/Linear_complementarity_problem

    with v the Lagrange multipliers on the non-negativity constraints, λ the multipliers on the inequality constraints, and s the slack variables for the inequality constraints. The fourth condition derives from the complementarity of each group of variables ( x , s ) with its set of KKT vectors (optimal Lagrange multipliers) being ( v , λ ) .