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Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization , some or all of the variables used in a discrete optimization problem are restricted to be discrete variables —that is, to assume only a discrete set of values, such as the integers .
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. [ 1 ] [ 2 ] It is generally divided into two subfields: discrete optimization and continuous optimization .
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [1] – do not vary smoothly in this way, but have distinct, separated values. [2]
Sequential minimal optimization; Sequential quadratic programming; Simplex algorithm; Simulated annealing; Simultaneous perturbation stochastic approximation; Social cognitive optimization; Space allocation problem; Space mapping; Special ordered set; Spiral optimization algorithm; Stochastic dynamic programming; Stochastic gradient Langevin ...
Hasse diagram of the search graph of the algorithm for 3 variables. Given e.g. the subset = {, ¯, ¯, ¯ ¯, ¯ ¯} of the bottom-level nodes (light green), the algorithm computes a minimal set of nodes (here: {¯,}, dark green) that covers exactly .
In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry.
Mathematical Optimization Society; Mathematical programming with equilibrium constraints; Max–min inequality; Maximum and minimum; Maximum theorem; MCACEA; Mean field annealing; Minimax theorem; Mirror descent; Mixed complementarity problem; Mixed linear complementarity problem; Moreau envelope; Multi-attribute global inference of quality