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We refer to second-order cone programs as deterministic second-order cone programs since data defining them are deterministic. Stochastic second-order cone programs are a class of optimization problems that are defined to handle uncertainty in data defining deterministic second-order cone programs. [10]
Second-order cone programming; Semidefinite embedding; Sequential linear-quadratic programming; Sequential minimal optimization; Sequential quadratic programming; Simplex algorithm; Simulated annealing; Simultaneous perturbation stochastic approximation; Social cognitive optimization; Space allocation problem; Space mapping; Special ordered set
On March 5, 2021, an edit titled "correct errors" removed an extremely useful formula. In particular, there used to be a formula for converting x T A T A x + b T x + c ≤ 0 {\displaystyle x^{T}A^{T}Ax+b^{T}x+c\leq 0} into an SOCP constraint, but it was replaced by a different one for x T A x + b T x + c ≤ 0 {\displaystyle x^{T}Ax+b^{T}x+c ...
Second-order cone programming (SOCP) is a convex program, and includes certain types of quadratic programs. Semidefinite programming (SDP) is a subfield of convex optimization where the underlying variables are semidefinite matrices. It is a generalization of linear and convex quadratic programming.
In mathematics, Abel's identity (also called Abel's formula [1] or Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation.
Equivalently, the second-order conditions that are sufficient for a local minimum or maximum can be expressed in terms of the sequence of principal (upper-leftmost) minors (determinants of sub-matrices) of the Hessian; these conditions are a special case of those given in the next section for bordered Hessians for constrained optimization—the ...
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A (existential second-order) formula is one additionally having some existential quantifiers over second order variables, i.e. …, where is a first-order formula. The fragment of second-order logic consisting only of existential second-order formulas is called existential second-order logic and abbreviated as ESO, as , or even as ∃SO.