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A second-order cone program (SOCP) ... SCS (Splitting Conic Solver) is a numerical optimization package for solving large-scale convex quadratic cone problems.
A commercial optimization solver for linear programming, non-linear programming, mixed integer linear programming, convex quadratic programming, convex quadratically constrained quadratic programming, second-order cone programming and their mixed integer counterparts. AMPL: CPLEX: Popular solver with an API for several programming languages.
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.
A hierarchy of convex optimization problems. (LP: linear programming, QP: quadratic programming, SOCP second-order cone program, SDP: semidefinite programming, CP: conic optimization.) Linear programming problems are the simplest convex programs. In LP, the objective and constraint functions are all linear. Quadratic programming are the next ...
The vertices of a central conic can be determined by calculating the intersections of the conic and its axes — in other words, by solving the system consisting of the quadratic conic equation and the linear equation for alternately one or the other of the axes. Two or no vertices are obtained for each axis, since, in the case of the hyperbola ...
A cone is a convex cone if + belongs to , for any positive scalars , , and any , in . [5] [6] A cone is convex if and only if +.This concept is meaningful for any vector space that allows the concept of "positive" scalar, such as spaces over the rational, algebraic, or (more commonly) the real numbers.
An equation (or set of equations) stating that the first derivative(s) equal(s) zero at an interior optimum is called a 'first-order condition' or a set of first-order conditions. Optima of equality-constrained problems can be found by the Lagrange multiplier method.
SOC – second order condition. Soln – solution. Sp – symplectic group. Sp – trace of a matrix, from the German "spur" used for the trace. sp, span – linear span of a set of vectors. (Also written with angle brackets.) Spec – spectrum of a ring. Spin – spin group. sqrt – square root. s.t. – such that or so that or subject to.
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