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  2. 80 of the Most Useful Excel Shortcuts - AOL

    www.aol.com/lifestyle/80-most-useful-excel...

    Minimize or maximize ribbon tabs. Command + Shift + Tab. ... Formatting and editing cells. Formatting cells using Excel shortcuts is a lot faster than choosing options from menus. These are the ...

  3. Reduced cost - Wikipedia

    en.wikipedia.org/wiki/Reduced_cost

    Given a system minimize subject to ,, the reduced cost vector can be computed as , where is the dual cost vector. It follows directly that for a minimization problem, any non- basic variables at their lower bounds with strictly negative reduced costs are eligible to enter that basis, while any basic variables must have a reduced cost that is ...

  4. Duality (optimization) - Wikipedia

    en.wikipedia.org/wiki/Duality_(optimization)

    Linear programming problems are optimization problems in which the objective function and the constraints are all linear. In the primal problem, the objective function is a linear combination of n variables. There are m constraints, each of which places an upper bound on a linear combination of the n variables. The goal is to maximize the value ...

  5. Multi-objective optimization - Wikipedia

    en.wikipedia.org/wiki/Multi-objective_optimization

    Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.

  6. Karush–Kuhn–Tucker conditions - Wikipedia

    en.wikipedia.org/wiki/Karush–Kuhn–Tucker...

    Consider the following nonlinear optimization problem in standard form: . minimize () subject to (),() =where is the optimization variable chosen from a convex subset of , is the objective or utility function, (=, …,) are the inequality constraint functions and (=, …,) are the equality constraint functions.

  7. Quadratic programming - Wikipedia

    en.wikipedia.org/wiki/Quadratic_programming

    Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions.Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables.