I'm 44 and my face looks gaunt and neck is sagging. What minimally invasive procedures would help?

your loss of volume can be improved using Voluma injectable filler. It is reliable and lasts two years. Fat sounds to patients better since it is permanent but very often patients end up with lumps and asymmetries which are very difficult to correct. A mini lift will also  help to remove excess skin in your face and or neck. See several very experienced facelift surgeons who will discuss with you the most minimal procedures as well as procedures that have actual merits so you don't waste your money. 

In order to improve the jawline and cheek hollows, I use a combination of VASER liposuction and thermiRF at the same time for this.  Noninvasive options such as thermage, ultherapy, kybella, and fillers can also be used.  Please get a formal consultation as in addition to the above,  lasers, microneedling/PRP can be used for texture tone and intensif microneedling/RF for fine lines and some tightening. Best, Dr. Emer.

Your pictures do demonstrate some loss of volume in the cheeks.  The main non-surgical option to improve this issue would be injectable fillers.  Adding volume to your cheeks would most likely improve some of the looseness you see along your jaw as well.  Your neck does not appear saggy to me, but there are some non-surgical skin tightening treatments such as Ultherapy or radio frequency that could potentially help.  

What you can see mostly in these pictures is some volume loss in the face.  The neck looks pretty good.  Your best bet would be either fat transfer or fillers to the cheeks.  this will help to replace the lost volume and will help to tighten up your jawline. 

To restore volume in the mid-face can be performed with fillers placed in that area in the office setting with to be minimally invasive, And temporary.  Cheek implants can offer a more permanent alternative. A revision rhinoplasty procedure can accomplish reduction of the significant hanging columella and alar retraction present. For more information and many examples of both procedures, please see the link and the video below