Jelaskan Teknik dari Optimisasi (matematik) dalam bahasa sunda

tehnik keur ngarengsekeun program matematik gumantung kana kondisi alami fungsi obyektif fungsi jeung constraint set. The following major subfields exist:

linear programming studies the case in which the objective function f is linéar and the set A is specified using only linéar equalities and inequalities

integer programming studies linéar programs in which some or all variables are constrained to take on integer values

quadratic programming allows the objective function to have quadratic terms, while the set A must be specified with linéar equalities and inequalities

nonlinear programming studies the general case in which the objective or constraints or both contain nonlinéar parts

program stokastik nalungtik kasus nu gumantung kana variabel acak

dynamic programming studies the case which has optimal substructure and overlapping subproblems.

For twice-differentiable functions, unconstrained problems can be solved by finding the places where the gradient of the function is 0 (i.e. the stationary points) and using the Hessian matrix to classify the type of point. If the hessian is positive definite, the point is a local minimum, if negative definite, a local maximum, and if indefinite it is some kind of saddle point.

Should a function be convex over a region of interest (as defined by constraints) then any local minimum will also be a global minimum. Robust, fast numerical techniques exist for optimizing doubly differentiable convex functions. Outside of these functions, less idéal techniques must be used.

Constrained problems can often be transformed into unconstrained problems with the help of the Lagrange multiplier.

Several techniques exist for find a good local minimum in nonlinéar optimization problems with many poor local minima: