Given a function, find an element so that for all a, (minimize); Or (maximize).
This formula is sometimes called "mathematical programming" (for example, linear programming). Many practical and theoretical problems can be modeled as such a general framework.
Generally, A is a subset of Euclidean space, which is usually defined by a constraint equation or inequality that A must satisfy. The elements of a are called feasible solutions. The function f is called the objective function or the cost function. The feasible solution to minimize (or maximize) the objective function is called the optimal solution.
Generally speaking, there are several local minima or maxima. The local minimum x * is defined as that for some δ >: 0, all x is satisfied.
}-;
formula
Established. That is to say, on some closed balls around, all the function values are greater than or equal to the function values of this point. Generally speaking, it is easy to find a local minimum, but to ensure that it is a global minimum, some additional conditions are needed, such as that the function must be convex.
branch
Linear Programming When the objective function F is a linear function and the set A is determined by a linear equality function and a linear inequality function, we call this kind of problem linear programming.
Integer Programming When some or all variables of a linear programming problem are limited to integer values, we call this kind of problem a bit integer programming problem.
The objective function of quadratic programming is quadratic function, and set A must be determined by linear equality function and linear inequality function.
Nonlinear programming studies the problem that the objective function or constraint function contains nonlinear functions.
Stochastic programming studies the problem that some variables are random variables.
Dynamic programming studies the optimization problem, that is, the optimal strategy is based on decomposing the problem into several smaller subproblems.
Combinatorial optimization studies whether the feasible solution is discrete or can be transformed into discrete.
Infinite dimensional optimization studies the problem that the set of feasible solutions is a subset of infinite dimensional space. An example of infinite dimensional space is function space.