I want an adjustable boost converter so I can use my USB Power Bank to power a portable radio that needs a supply of 7.5V.

I can probably use a 555 IC such as this circuit which boosts 3V to 9V.

I replaced the potmeter with a 50k as I did not have a 20k in my inventory.

This is measured directly on the base of the transistor. Supply voltage is around 3V. The output on the other side of the diode is a pretty clean 3V DC. I tried several different inductors but none seems to increase the voltage much beyond +0.5V above the supply. Turning the potmeter has a great impact on the frequency, changing it between around 25-400 kHz.

What is the optimal frequency for a boost converter?

Maybe this document Basic Calculation of a Boost Converter's Power Stage by TI is a good idea to study? No, the formula steps require a 'converter IC'.

I measured the current draw of the radio, which seems to be around 20mA. To emulate this I will use an $R = {U \over I}={7.5 \over 0.02} = 375 \ohm$?? resistor. Sadly, after installing this 'load' I am unable to achieve any voltage above the input.

This might be helpful? Four Tips to Debug a Boost Converter (by TI) No, not really.

FAILED I am unable to achieve a voltage higher then the input of 5V, after having tried swapping most of the components. Next I will try with a MOSFET.

But wait...I may have connected the diode wrong on my breadboard...wil try again.

Also, improved breadboard design with fewer wires:

Nope, no matter what I try I cannot get the output above 4.3V with the load attached.