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Constrained optimization. In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to ...
In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear programming to be optimal, provided that some regularity conditions are satisfied. Allowing inequality constraints, the ...
Mathematical programming with equilibrium constraints (MPEC) is the study of constrained optimization problems where the constraints include variational inequalities or complementarities. MPEC is related to the Stackelberg game. MPEC is used in the study of engineering design, economic equilibrium, and multilevel games.
Lagrange multiplier. In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1]
Constraint programming. Constraint programming (CP)[1] is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables.
Constraint satisfaction. In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution through a set of constraints that impose conditions that the variables must satisfy. [1] A solution is therefore an assignment of values to the variables that satisfies all constraints—that is, a point in ...
The complexity of constraint satisfaction is the application of computational complexity theory to constraint satisfaction. It has mainly been studied for discriminating between tractable and intractable classes of constraint satisfaction problems on finite domains. Solving a constraint satisfaction problem on a finite domain is an NP-complete ...
Constraint (mathematics) In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set.