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A second-order cone program (SOCP) is a convex optimization problem of the form . minimize subject to ‖ + ‖ +, =, …, = where the problem parameters are ...
The following problem classes are all convex optimization problems, or can be reduced to convex optimization problems via simple transformations: [7]: chpt.4 [10] A hierarchy of convex optimization problems. (LP: linear programming, QP: quadratic programming, SOCP second-order cone program, SDP: semidefinite programming, CP: conic optimization.)
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.
Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine subspace and a convex cone. The class of conic optimization problems includes some of the most well known classes of convex optimization problems, namely linear and semidefinite programming .
Newton's method uses curvature information (i.e. the second derivative) to take a more direct route. In calculus , Newton's method (also called Newton–Raphson ) is an iterative method for finding the roots of a differentiable function f {\displaystyle f} , which are solutions to the equation f ( x ) = 0 {\displaystyle f(x)=0} .
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.
This category corresponds roughly to MSC 90C25 Convex programming; see 90C25 at MathSciNet and 90C25 at zbMATH. Pages in category "Convex optimization" The following 41 pages are in this category, out of 41 total.
Traditional envelope theorem derivations use the first-order condition for , which requires that the choice set have the convex and topological structure, and the objective function be differentiable in the variable . (The argument is that changes in the maximizer have only a "second-order effect" at the optimum and so can be ignored.)