It is not in Our [the Self's] control to acquire or to renounce. They are both [activities] of the non-Self and are subject to external factors such as scientific circumstantial evidences.

Renunciation and saiyam are two different things. Renunciation is where one gives up all marital ties, parental ties, financial ties and material possessions. What is saiyam? When anger, pride, deceit, greed and attachment-abhorence are under control, then it is considered as saiyam. 

What is saiyam? It is a state in which One remains unaffected by the effects of both, upsarga (externally induced suffering) and parishaha (internally induced affliction). And if one were to get affected, then One would simply continue to Know the effect but would not suffer (vedey) the effect. And even if he were to suffer the effect, He would still simply Know it; that is known as saiyam.     

As long as one does not have Knowledge of the Self, his renunciation (tyaag) will give result. And after attaining the Knowledge of the Self, there is no renunciation; there is only a vow (vrat). A vow is that which prevails on its own.    

The Lord used to See His own penance Himself! 

Where there is no solution, there One should keep Seeing-Knowing. If one has not attained Atmagnan (Knowledge of the Self), even then he can keep seeing through indriya gnan (knowledge attained through the medium of the sense organs). However, there is a difference between seeing through indriya gnan and Seeing through the Knowledge of the Self. In seeing through indriya gnan, egoism is present!

What is the direct cause of liberation? Dwelling in the Self (Swaramanata). The entire world dwells in the non-Self (par-ramanata).

Atma ramanata (dwelling in the Self) arises after experiencing the Self, until then Atma ramanata cannot arise at all.

Envisioning that, 'I am Atma (the Self) and these are my guna-dharmas (intrinsic properties that have a specific function)'; that is to prevail in one's real form (Swaroop) and intrisic nature (Swabhaav) is Swaramanata (dwelling as the Self).