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</math>We assume that the constraint functions belong to some family (e.g. quadratic functions), so that the program can be represented by a finite ''vector of coefficients'' (e.g. the coefficients to the quadratic functions). The dimension of this coefficient vector is called the ''size'' of the program. A ''numerical solver'' for a given family of programs is an algorithm that, given the coefficient vector, generates a sequence of approximate solutions ''x<sub>t</sub>'' for ''t''=1,2,..., using finitely many arithmetic operations. A numerical solver is called ''convergent'' if, for any program from the family and any positive ''ε''>0, there is some ''T'' (which may depend on the program and on ''ε'') such that, for any ''t''>''T'', the approximate solution ''x<sub>t</sub>'' is ''ε-approximate,'' that is:
\begin{aligned}
f(x_{t
g_{i}(x_{t} \leq \epsilon \, \text{for} \, i = 1, \dots, m, \\
''x'' in ''G'',
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