16 results about "Second-order cone programming" patented technology

A second-order cone program (SOCP) is a convex optimization problem of the form minimize fᵀx subject to ∥Aᵢx+bᵢ∥₂≤cᵢᵀx+dᵢ, i=1,…,m Fx=g where the problem parameters are f∈ℝⁿ, Aᵢ∈ℝⁿᵢ×ⁿ, bᵢ∈ℝⁿᵢ, cᵢ∈ℝⁿ, dᵢ∈ℝ, F∈ℝᵖ×ⁿ, and g∈ℝᵖ. x∈ℝⁿ is the optimization variable. ∥x∥₂ is the Euclidean norm and ᵀ indicates transpose. When Aᵢ=0 for i=1,…,m, the SOCP reduces to a linear program. When cᵢ=0 for i=1,…,m, the SOCP is equivalent to a convex quadratically constrained linear program.