Equality constraints are conditions that specify that certain relationships among variables must be exactly satisfied in optimization problems. In the context of nonlinear programming, these constraints play a vital role in defining the feasible region for a solution, ensuring that specific requirements or limits are met while optimizing an objective function. They are often expressed in the form of equations, such as $$h_i(x) = 0$$, where $$h_i$$ represents a constraint function and $$x$$ is the vector of decision variables.
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