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Linear-fractional programming — objective is ratio of linear functions, constraints are linear Fractional programming — objective is ratio of nonlinear functions, constraints are linear; Nonlinear complementarity problem (NCP) — find x such that x ≥ 0, f(x) ≥ 0 and x T f(x) = 0; Least squares — the objective function is a sum of squares
Given an initial assignment of values to all the variables of a constraint satisfaction problem (with one or more constraints not satisfied), select a variable from the set of variables with conflicts violating one or more of its constraints. Assign to this variable a value that minimizes the number of conflicts (usually breaking ties randomly).
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables , which is solved by constraint satisfaction methods.
Alternatively, if the constraints are all equality constraints and are all linear, they can be solved for some of the variables in terms of the others, and the former can be substituted out of the objective function, leaving an unconstrained problem in a smaller number of variables.
If the objective function is quadratic and the constraints are linear, quadratic programming techniques are used. If the objective function is a ratio of a concave and a convex function (in the maximization case) and the constraints are convex, then the problem can be transformed to a convex optimization problem using fractional programming ...
The nurse scheduling problem (NSP), also called the nurse rostering problem (NRP), is the operations research problem of finding an optimal way to assign nurses to shifts, typically with a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative quality of valid solutions. [1]
Constraints may involve institutional review boards, informed consent and confidentiality affecting both clinical (medical) trials and behavioral and social science experiments. [42] In the field of toxicology, for example, experimentation is performed on laboratory animals with the goal of defining safe exposure limits for humans. [43]
Optimal control problem benchmark (Luus) with an integral objective, inequality, and differential constraint. Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. [1]