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The goal is to pick a subset F of facilities to open, to minimize the sum of distances from each demand point to its nearest facility, plus the sum of opening costs of the facilities. The facility location problem on general graphs is NP-hard to solve optimally, by reduction from (for example) the set cover problem. A number of approximation ...
Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance (related to the pricing of American options). A key example of an optimal stopping problem is the secretary problem.
The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as the special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal.
The MM algorithm is an iterative optimization method which exploits the convexity of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a minimization or a maximization.
Many optimization problems can be equivalently formulated in this standard form. For example, the problem of maximizing a concave function can be re-formulated equivalently as the problem of minimizing the convex function . The problem of maximizing a concave function over a convex set is commonly called a convex optimization problem.
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.
Excel's storage of numbers in binary format also affects its accuracy. [3] To illustrate, the lower figure tabulates the simple addition 1 + x − 1 for several values of x. All the values of x begin at the 15 th decimal, so Excel must take them into account. Before calculating the sum 1 + x, Excel first approximates x as a binary number
After the problem on variables +, …, is solved, its optimal cost can be used as an upper bound while solving the other problems, In particular, the cost estimate of a solution having x i + 1 , … , x n {\displaystyle x_{i+1},\ldots ,x_{n}} as unassigned variables is added to the cost that derives from the evaluated variables.