I’ll speak about Augustine since I am knowledgeable about him. Augustine did in fact believe that God deliberately chose not to save everyone, but only a few. In his work On the Predestination of Saints he wrote the following (Chapter 8; paragraph 14):
“Why does he [God] not teach all, so that they might come to Christ? Perhaps because all those he teaches in mercy [he taught]; but those who he does not teach in justice he does not teach [at all]? Because 'he has mercy on whom he wills, and whomever he wills he hardens. (Romans 9:18)… Thus rightly we say, God leads all to come to Christ, not because they all come [on their own accord], but because no one in any other matter [is able] to come. But why does he not teach all? The Apostle made it abundantly clear: because ‘wanting to show his anger, and his power, he endured with much patience the vessels of wrath who are made for perdition, and so that he might make [some] signs of his divine glory with the vessels of mercy, who he prepared in glory’ (Romans 9:18-23). Hence it is that ‘the word of the cross is foolishness to those who are perishing, but to us who are saved it is the power of God. (1 Corinthians 1:18).’ Here God teaches all to come to Christ; for here ‘he wishes all to be saved, and to come to knowledge in truth’ (1 Timothy 2:4). For if God wished to teach those whom the word of the cross is foolishness so that they might come to Christ, undoubtedly they too would have come. For he does not deceive nor is deceived when he says, ‘All who have heard from the Father and have learned, come to me’ (John 6:45). Therefore, perish the thought that anyone does not come who has heard from the Father and has learned.”
Cur ergo non omnes docet, ut veniant ad Christum; nisi quia omnes quos docet, misericordia docet; quos autem non docet, judicio non docet? Quoniam cujus vult miseretur, et quem vult obdurat: sed miseretur, bona tribuens; obdurat, digna retribuens. Aut si et ista, ut quidam distinguere maluerunt, verba sunt ejus cui Apostolus ait, Dicis itaque mihi: ut ipse dixisse accipiatur, Ergo cujus vult miseretur, et quem vult obdurat; et quae sequuntur, id est, Quid adhuc conqueritur? nam voluntati ejus quis resistit? numquid responsum est ab Apostolo, O homo, falsum est quod dixisti? Non: sed responsum est, O homo, tu quis es qui respondeas Deo? Numquid dicit figmentum ei qui se finxit, Quare sic me fecisti? Annon habet potestatem figulus luti ex eadem massa, et sequentia, quae optime nostis. Et tamen secundum quemdam modum, omnes Pater docet venire ad suum Filium. Non enim frustra scriptum est in Prophetis, Et erunt omnes docibiles Dei. Quod testimonium cum praemisisset, tunc subdidit, Omnis qui audivit a Patre et didicit, venit ad me. Sicut ergo integre loquimur, cum de aliquo litterarum magistro, qui in civitate solus est, dicimus, Omnes iste hic litteras docet; non quia omnes discunt, sed quia nemo nisi ab illo discit, quicumque ibi litteras discit: ita recte dicimus, Omnes Deus docet venire ad Christum, non quia omnes veniunt, sed quia nemo aliter venit. Cur autem non omnes doceat, aperuit Apostolus, quantum aperiendum judicavit: quia volens ostendere iram, et demonstrare potentiam suam, attulit in multa patientia vasa irae quae perfecta sunt in perditionem, et ut notas faciat divitias gloriae suae in vasa misericordiae, quae praeparavit in gloriam (Rom. IX, 18-23). Hinc est quod verbum crucis pereuntibus stultitia est; his autem qui salvi fiunt, virtus Dei est (I Cor. I, 18). Hos omnes docet venire au Christum Deus; hos enim omnes vult salvos fieri, et in agnitionem veritatis venire (I Tim. II, 4). Nam si et illos quibus stultitia est verbum crucis, ut ad Christum venirent, docere voluisset, procul dubio venirent et ipsi. Non enim fallit aut fallitur qui ait, Omnis qui audivit a Patre et didicit, venit ad me. Absit ergo ut quisquam non veniat, qui a Patre audivit et didicit.
I highlighted the portions that I translated.
Gerald Bonner, a Patristics scholar, has some really good work on Augustine’s theories of grace, free will, and salvation. I can give you the bibliographic information if you want.