Search results
Results from the WOW.Com Content Network
The "second-order cone" in SOCP arises from the constraints, which are equivalent to requiring the affine function (+, +) to lie in the second-order cone in +. [ 1 ] SOCPs can be solved by interior point methods [ 2 ] and in general, can be solved more efficiently than semidefinite programming (SDP) problems. [ 3 ]
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.
Download as PDF; Printable version; ... Barrier function; Biconvex optimization; ... Second-order cone programming; Semidefinite programming;
In LP, the objective and constraint functions are all linear. Quadratic programming are the next-simplest. In QP, the constraints are all linear, but the objective may be a convex quadratic function. Second order cone programming are more general. Semidefinite programming are more general. Conic optimization are even more general - see figure ...
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
The IBM ILOG CPLEX Optimizer solves integer programming problems, very large [3] linear programming problems using either primal or dual variants of the simplex method or the barrier interior point method, convex and non-convex quadratic programming problems, and convex quadratically constrained problems (solved via second-order cone programming, or SOCP).
For very simple problems, say a function of two variables subject to a single equality constraint, it is most practical to apply the method of substitution. [4] The idea is to substitute the constraint into the objective function to create a composite function that incorporates the effect of the
Zero-order routines - use only the values of the objective function and constraint functions at the current point; First-order routines - use also the values of the gradients of these functions; Second-order routines - use also the values of the Hessians of these functions. Third-order routines (and higher) are theoretically possible, but not ...