This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

MinValue

MinValue
gives the minimum value of f with respect to x.
MinValue
gives the minimum value of f with respect to x, y, ....
MinValue
gives the minimum value of f subject to the constraints cons.
MinValue
gives the minimum value of f over the domain dom, typically Reals or Integers.
  • MinValue gives the infimum of values of f. It may not be attained for any values of x, y, ....
  • cons can contain equations, inequalities, or logical combinations of these.
  • If f and cons are linear or polynomial, MinValue will always find a global minimum.
  • MinValue will return exact results if given exact input.
  • If MinValue is given an expression containing approximate numbers, it automatically calls NMinValue.
  • If no domain is specified, all variables are assumed to be real.
  • Integers can be used to specify that a particular variable can take on only integer values.
Find the minimum value of a univariate function:
Find the minimum value of a multivariate function:
Find the minimum value of a function subject to constraints:
Find the minimum value as a function of parameters:
Find the minimum value of a univariate function:
In[1]:=
Click for copyable input
Out[1]=
 
Find the minimum value of a multivariate function:
In[1]:=
Click for copyable input
Out[1]=
 
Find the minimum value of a function subject to constraints:
In[1]:=
Click for copyable input
Out[1]=
 
Find the minimum value as a function of parameters:
In[1]:=
Click for copyable input
Out[1]=
Unconstrained univariate polynomial minimization:
Constrained univariate polynomial minimization:
Univariate transcendental minimization:
Univariate piecewise minimization:
Multivariate linear constrained minimization:
Linear-fractional constrained minimization:
Unconstrained polynomial minimization:
Constrained polynomial optimization can always be solved:
The minimum value may not be attained:
The objective function may be unbounded:
There may be no points satisfying the constraints:
Algebraic minimization:
Bounded transcendental minimization:
Piecewise minimization:
Unconstrained parametric minimization:
Constrained parametric minimization:
Integer linear programming:
Polynomial minimization over the integers:
Finding the exact minimum takes a long time due to high-degree algebraic number operations:
With WorkingPrecision, the result is an exact minimum value, but it might be incorrect:
Find the minimal perimeter among rectangles with a unit area:
Find the minimal perimeter among triangles with a unit area:
Find the distance to a parabola from a point on its axis:
Assuming a particular relationship between the and parameters:
Minimize gives both the value of the minimum and the minimizer point:
For strict polynomial inequality constraints MinValue may be much faster than Minimize:
MinValue gives an exact global minimum value of the objective function:
NMinValue attempts to find a global minimum numerically, but may find a local minimum:
FindMinValue finds local minima depending on the starting point:
MinValue can solve linear programming problems:
LinearProgramming can be used to solve the same problem given in matrix notation:
MinValue requires that all functions present in the input be real valued:
Values for which the equation is satisfied but the square roots are not real are disallowed:
New in 7