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  2. LP-type problem - Wikipedia

    en.wikipedia.org/wiki/LP-type_problem

    In this formulation, the set S is the set of all vertices in both polytopes, and the function value f(A) is the negation of the smallest distance between the convex hulls of the two subsets A of vertices in the two polytopes. The combinatorial dimension of the problem is d + 1 if the two polytopes are disjoint, or d + 2 if they have a nonempty ...

  3. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    Let S 1 be the selling price of wheat and S 2 be the selling price of barley, per hectare. If we denote the area of land planted with wheat and barley by x 1 and x 2 respectively, then profit can be maximized by choosing optimal values for x 1 and x 2. This problem can be expressed with the following linear programming problem in the standard form:

  4. Linear-fractional programming - Wikipedia

    en.wikipedia.org/wiki/Linear-fractional_programming

    A linear program can be regarded as a special case of a linear-fractional program in which the denominator is the constant function 1. Formally, a linear-fractional program is defined as the problem of maximizing (or minimizing) a ratio of affine functions over a polyhedron ,

  5. Dual linear program - Wikipedia

    en.wikipedia.org/wiki/Dual_linear_program

    We use this example to illustrate the proof of the weak duality theorem. Suppose that, in the primal LP, we want to get an upper bound on the objective 3 x 1 + 4 x 2 {\displaystyle 3x_{1}+4x_{2}} . We can use the constraint multiplied by some coefficient, say y 1 {\displaystyle y_{1}} .

  6. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons , quarks , gauge bosons and the Higgs boson .

  7. Revised simplex method - Wikipedia

    en.wikipedia.org/wiki/Revised_simplex_method

    For the rest of the discussion, it is assumed that a linear programming problem has been converted into the following standard form: =, where A ∈ ℝ m×n.Without loss of generality, it is assumed that the constraint matrix A has full row rank and that the problem is feasible, i.e., there is at least one x ≥ 0 such that Ax = b.

  8. 'We can work with him': Abortion opponents tentatively ... - AOL

    www.aol.com/him-abortion-opponents-tentatively...

    Examples include a recent proposal to make over-the-counter birth control free, as well as Biden’s executive order in August 2022 to support people who travel out of state for an abortion. The ...

  9. Fundamental theorem of linear programming - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    In mathematical optimization, the fundamental theorem of linear programming states, in a weak formulation, that the maxima and minima of a linear function over a convex polygonal region occur at the region's corners.