# Z94.1 - Analytical Techniques & Operations Research Terminology

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NASH-HARSONYI BARGAINING MODEL. A model of an n person bargaining game based on Nash’s axioms of collective rationality, symmetry, linear invariance, and solution location.

N-PERSON GAME. A multiperson game in which the success of (pay off to) each player depends not only on his actions but also on those of the other players.

NEAR-OPTIMUM SOLUTION. A feasible solution to a mathematical programming problem whose value of the objective function can be shown to be near the optimum value. 

NEGATIVE DEFINITE OR SEMIDEFINITE QUADRATIC FORM. XTAX is negative definite (semi-definite) if -XTAX is positive definite (semidefinite). 

NETWORK FLOW PROBLEM. (See MAXIMAL NETWORK FLOW PROBLEM.)

NODE. One of the defining points of a network; a junction point joined to some or all of the others by arcs. 

NONBASIC VARIABLE. A variable in a solution to a linear programming problem obtained by the simplex method and whose value has been arbitrarily set to equal zero. 

NONCONFORMITY. A departure of a quality characteristic from its intended level or state that occurs with a severity sufficient to cause an associated product or service not to meet a specification requirement.

NONDEGENERACY ASSUMPTION. The assumption that all basic feasible solutions to a linear programming problem are nondegenerate. This assumption is convenient in some proofs which demonstrate the finiteness and convergence of the simplex algorithm. 

NONDEGENERATE FEASIBLE SOLUTION. A basic feasible solution in which all of    the basic variables are positive. 

NONEGATIVITY CONSTRAINT. A restriction that a variable can take on only positive or zero values, e.g., x ≥ 0- 

NONLINEAR CONSTRAINT. A constraint which contains variables whose relationship cannot be expressed in terms of linear combinations. 

NONLINEAR EQUATION. An equation at least one of whose terms is a nonlinear function of the variables. 

NONLINEAR FUNCTION. A function defined as something other than a sum of terms consisting of a constant times a single variable plus a final constant; net, not a linear function. 

NONLINEAR PROGRAMMING. An inclusive term covering all types of constrained optimization problems except those where the objective function and the constraints are all linear. Special types of nonlinear programming for which some theory has been developed are convex programming, concave programming, and quadratic programming. 

NONSINGULAR MATRIX. A square matrix whose determinant is not zero, and thus whose rank (number of linearly independent columns) is equal to its dimension (number of rows). Any nonsingular matrix has an inverse. 

NORTHWEST CORNER RULE. A procedure for determining a first basic feasible solution to a transportation problem. 

NT-HARD PROBLEMS. Problems for which the algorithms known to solve the problem do so in a time proportional to an exponential function of the value of a measure of problem size or complexity.

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