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A function where the line segment between any two points on the graph of the function lies above or on the graph. In the context of nonlinear programming, if the objective function and constraints are convex, the problem is easier to solve, and any local minimum is also a global minimum.

These are equations or inequalities that define the feasible region in which the solution to the optimization problem must lie. In nonlinear programming, these can be nonlinear as well.

The lowest value of the objective function over the entire feasible region. In the context of nonlinear programming, finding the global minimum can be challenging due to the presence of multiple local minima.

The function that is being optimized (maximized or minimized) in a nonlinear programming problem. It is significant because it provides the measure of performance for the decision variables involved.

A set of first-order necessary conditions for a solution in nonlinear programming to be optimal, given certain regularity conditions. These conditions extend the method of Lagrange multipliers.

A point in the domain of the objective function where it has a lower value than at all nearby points in the feasible region. While a local minimum is of interest, it may not necessarily be the best solution in nonlinear programming.

Refers to the concept that optimization problems can be viewed from either the primal (original problem) or dual (derived problem) perspective. The duality in nonlinear programming allows us to gain insights into the structure of the problem and derive bounds for the objective function values.

A type of optimization problem where either the objective function or the constraints, or both, are nonconvex. These problems are significant in nonlinear programming due to their complexity and the potential for multiple local optima.

A function that combines the objective function and the constraints using Lagrange multipliers. It is significant as it is used to find the saddle points which can lead to optimal solutions for the constrained problem.