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m clean up spacing around commas and other punctuation fixes, replaced: ,t → , t, ,w → , w |
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\text{subject to}\quad & g_i(x) \leq 0 \text{ for } i = 1, \dots, m. \\
\end{aligned}
</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
''g<sub>i</sub>''(''x_t'') ≤ ''ε'' for ''i'' in 1,...,''m'',
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