Can I sprint without running out of stamina?

Yes, actually there is.

It's worth turning on the Stamina Bar display in the options for this technique.

If you hold the run button down (PS4 Circle in Control Set A), for a whole stamina bar, then just as it's about to empty, let go of the run button, and immediately hold it down again.

When done correctly, Noctis will flash green, do a little 'shimmy dash' and your stamina bar will refill.

There's some buffs earned with Ignis cooking that could give you infinite stamina:

• Sizzling Humongo-Steak
• Smoked Dualhorn Shank
• Thick and Juicy Steak
• Smoked Behemoth
• Royal Round Paella
• Crispy Cheese Pizza

Find the location in the source link below.

Source: http://fenixbazaar.com/2016/12/02/final-fantasy-xv-food-and-recipes-guide-all-effects-and-ingredients/