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ArgMax

ArgMax
gives a position at which f is maximized.
ArgMax
gives a position at which f is maximized.
ArgMax
gives a position at which f is maximized subject to the constraints cons.
ArgMax
gives a position at which f is maximized over the domain dom, typically Reals or Integers.
MORE INFORMATION
  • cons can contain equations, inequalities, or logical combinations of these.
  • If f and cons are linear or polynomial, ArgMax will always find a global maximum.
  • ArgMax will return exact results if given exact input.
  • If ArgMax is given an expression containing approximate numbers, it automatically calls NArgMax.
  • If the maximum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, ArgMax 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.
  • If the constraints cannot be satisfied, ArgMax returns .
EXAMPLESCLOSE ALL
Basic Examples   (4)
Find a maximizer point for a univariate function:
Find a maximizer point for a multivariate function:
Find a maximizer point for a function subject to constraints:
Find a maximizer point as a function of parameters:
Find a maximizer point for a univariate function:
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Find a maximizer point for a multivariate function:
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Find a maximizer point for a function subject to constraints:
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Find a maximizer point as a function of parameters:
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Scope   (15)
Unconstrained univariate polynomial maximization:
Constrained univariate polynomial maximization:
Univariate transcendental maximization:
Univariate piecewise maximization:
Multivariate linear constrained maximization:
Linear-fractional constrained maximization:
Unconstrained polynomial maximization:
Constrained polynomial optimization can always be solved:
Algebraic maximization:
Bounded transcendental maximization:
Piecewise maximization:
Unconstrained parametric maximization:
Constrained parametric maximization:
Integer linear programming:
Polynomial maximization over the integers:
Options   (1)
Finding an exact maximum point can take a long time:
With WorkingPrecision, you get an approximate maximum point:
Applications   (3)
Find the lengths of sides of a unit perimeter rectangle with the maximal area:
Find the lengths of sides of a unit perimeter triangle with the maximal area:
Find the time at which a projectile reaches the maximum height:
Properties & Relations   (4)
Maximize gives both the value of the maximum and the maximizer point:
ArgMax gives an exact global minimizer point:
NArgMax attempts to find a global maximizer numerically, but may find a local maximizer:
FindArgMax finds a local maximizer point depending on the starting point:
The maximum point satisfies the constraints, unless messages say otherwise:
The given point maximizes the distance from the point .
When the maximum is not attained, ArgMax may give a point on the boundary:
Here the objective function tends to the maximum value when y tends to infinity:
ArgMax can solve linear programming problems:
LinearProgramming can be used to solve the same problem given in matrix notation:
Possible Issues   (2)
The maximum value may not be attained:
The objective function may be unbounded:
There may be no points satisfying the constraints:
ArgMax 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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