optimization

(noun)

the design and operation of a system or process to make it as good as possible in some defined sense

Related Terms

  • cuboid
  • stochastic

Examples of optimization in the following topics:

  • Optimization

    • This application is called design optimization.
    • Economics is closely linked to optimization of agents.
    • Modern optimization theory includes traditional optimization theory but also overlaps with game theory and the study of economic equilibria.
    • Asset prices are also modeled using optimization theory, though the underlying mathematics relies on optimizing stochastic processes rather than on static optimization.
    • The optimization of market portfolios is an example of multi-objective optimization in economics.
  • Optimization in Several Variables

    • To solve an optimization problem, formulate the function $f(x,y, \cdots )$ to be optimized and find all critical points first.
    • An optimization process that involves only a single variable is rather straightforward.
    • The same strategy applies for optimization with several variables.
    • In this atom, we will solve a simple example to see how optimization involving several variables can be achieved.
    • Therefore, the goal of the optimization is to minimize a function $S(x,y,z) = 2(xy + yz+zx)$.
  • Lagrange Multiplers

    • In mathematical optimization, the method of Lagrange multipliers (named after Joseph Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints.
    • For instance, consider the following optimization problem: Maximize $f(x,y)$ subject to $g(x,y)=c$.
    • Thus, the method of Lagrange multipliers yields a necessary condition for optimality in constrained problems.
  • Maximum and Minimum Values

    • Finding global maxima and minima is the goal of mathematical optimization.
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