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ArgMin

ArgMin
gives a position at which f is minimized.
ArgMin
gives a position at which f is minimized.
ArgMin
gives a position at which f is minimized subject to the constraints cons.
ArgMin
gives a position at which f is minimized over the domain dom, typically Reals or Integers.
MORE INFORMATION
  • ArgMin returns a list of the form .
  • cons can contain equations, inequalities, or logical combinations of these.
  • If f and cons are linear or polynomial, ArgMin will always find a global minimum.
  • ArgMin will return exact results if given exact input.
  • If ArgMin is given an expression containing approximate numbers, it automatically calls NArgMin.
  • If the minimum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, ArgMin will return the closest specifiable point.
  • 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.
EXAMPLESCLOSE ALL
Basic Examples   (4)
Find a minimizer point for a univariate function:
Find a minimizer point for a multivariate function:
Find a minimizer point for a function subject to constraints:
Find a minimizer point as a function of parameters:
Find a minimizer point for a univariate function:
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Find a minimizer point for a multivariate function:
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Find a minimizer point for a function subject to constraints:
In[1]:=
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Out[1]=
 
Find a minimizer point as a function of parameters:
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Out[1]=
Scope   (15)
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:
Algebraic minimization:
Bounded transcendental minimization:
Piecewise minimization:
Unconstrained parametric minimization:
Constrained parametric minimization:
Integer linear programming:
Polynomial minimization over the integers:
Options   (1)
Finding an exact minimum point can take a long time:
With WorkingPrecision, you get an approximate minimum point:
Applications   (3)
Find the lengths of sides of a unit area rectangle with minimal perimeter:
Find the lengths of sides of a unit area triangle with minimal perimeter:
The minimal perimeter triangle is equilateral:
Find a point on a parabola closest to its axis:
Assuming a particular relationship between the and parameters:
Properties & Relations   (5)
Minimize gives both the value of the minimum and the minimizer point:
ArgMin gives an exact global minimizer point:
NArgMin attempts to find a global minimizer point numerically, but may find a local minimizer:
FindArgMin finds a local minimizer point depending on the starting point:
The minimum point satisfies the constraints, unless messages say otherwise:
The given point minimizes the distance from the point :
When the minimum is not attained, ArgMin may give a point on the boundary:
Here the objective function tends to the minimum value when y tends to infinity:
ArgMin can solve linear programming problems:
LinearProgramming can be used to solve the same problem given in matrix notation:
Possible Issues   (2)
A finite minimum value may not be attained:
The objective function may be unbounded:
There may be no points satisfying the constraints:
ArgMin 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:
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