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  2. Mathematical optimization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_optimization

    Infinite-dimensional optimization studies the case when the set of feasible solutions is a subset of an infinite-dimensional space, such as a space of functions. Heuristics and metaheuristics make few or no assumptions about the problem being optimized. Usually, heuristics do not guarantee that any optimal solution need be found.

  3. Convex optimization - Wikipedia

    en.wikipedia.org/wiki/Convex_optimization

    the optimal set is convex; if the objective function is strictly convex, then the problem has at most one optimal point. These results are used by the theory of convex minimization along with geometric notions from functional analysis (in Hilbert spaces) such as the Hilbert projection theorem, the separating hyperplane theorem, and Farkas' lemma.

  4. Heuristic (computer science) - Wikipedia

    en.wikipedia.org/wiki/Heuristic_(computer_science)

    TSP is known to be NP-hard so an optimal solution for even a moderate size problem is difficult to solve. Instead, the greedy algorithm can be used to give a good but not optimal solution (it is an approximation to the optimal answer) in a reasonably short amount of time. The greedy algorithm heuristic says to pick whatever is currently the ...

  5. Optimization problem - Wikipedia

    en.wikipedia.org/wiki/Optimization_problem

    The goal is then to find for some instance x an optimal solution, that is, a feasible solution y with (,) = {(, ′): ′ ()}. For each combinatorial optimization problem, there is a corresponding decision problem that asks whether there is a feasible solution for some particular measure m 0 .

  6. Satisficing - Wikipedia

    en.wikipedia.org/wiki/Satisficing

    A solution s ∈ X to this optimization problem is optimal if, and only if, it is a satisficing option (an element of S). Thus, from a decision theory point of view, the distinction between "optimizing" and "satisficing" is essentially a stylistic issue (that can nevertheless be very important in certain applications) rather than a substantive ...

  7. Simplex algorithm - Wikipedia

    en.wikipedia.org/wiki/Simplex_algorithm

    The simplex algorithm can then be applied to find the solution; this step is called Phase II. If the minimum is positive then there is no feasible solution for the Phase I problem where the artificial variables are all zero. This implies that the feasible region for the original problem is empty, and so the original problem has no solution.

  8. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    However, some problems have distinct optimal solutions; for example, the problem of finding a feasible solution to a system of linear inequalities is a linear programming problem in which the objective function is the zero function (i.e., the constant function taking the value zero everywhere).

  9. Greedy algorithm - Wikipedia

    en.wikipedia.org/wiki/Greedy_algorithm

    Greedy algorithms fail to produce the optimal solution for many other problems and may even produce the unique worst possible solution. One example is the travelling salesman problem mentioned above: for each number of cities, there is an assignment of distances between the cities for which the nearest-neighbour heuristic produces the unique ...