Second-Order Cone Programming
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High Quality Content by WIKIPEDIA articles! A second-order cone program (SOCP) is a convex optimization problem of the formwhere the problem parameters are f in mathbb{R}^n, A_i in mathbb{R}^{{n_i}times n}, b_i in mathbb{R}^{n_i}, c_i in mathbb{R}^n, d_i in mathbb{R}, F in mathbb{R}^{ptimes n}, and g in mathbb{R}^p. Here xinmathbb{R}^n is the optimization variable. When Ai = 0 for i = 1,dots,m, the SOCP reduces to a linear program. When ci = 0 for i = 1,dots,m, the SOCP is equivalent to a convex Quadratically constrained quadratic program. Semidefinite programs subsumes SOCPs as the SOCP const...
High Quality Content by WIKIPEDIA articles! A second-order cone program (SOCP) is a convex optimization problem of the formwhere the problem parameters are f in mathbb{R}^n, A_i in mathbb{R}^{{n_i}times n}, b_i in mathbb{R}^{n_i}, c_i in mathbb{R}^n, d_i in mathbb{R}, F in mathbb{R}^{ptimes n}, and g in mathbb{R}^p. Here xinmathbb{R}^n is the optimization variable. When Ai = 0 for i = 1,dots,m, the SOCP reduces to a linear program. When ci = 0 for i = 1,dots,m, the SOCP is equivalent to a convex Quadratically constrained quadratic program. Semidefinite programs subsumes SOCPs as the SOCP constraints can be written as Linear Matrix Inequalities(LMI) and can be reformulated as an instance of semi definite program. SOCPs can be solved with great efficiency by interior point methods.
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