Choosing an Efficient V Reg. Configuration for Dynamic Supply V and Load Current

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Choosing Efficient Volt. Reg. Configuration for Dynamic Supply V and Load Current

My goal is to charge a super capacitor C1 (30mF) from an unregulated voltage source Vbat via a voltage regulator (or a bunch of them) V_REG in an efficient way (say 85% efficiency and above). With the following constraints:

    1) At any given time voltage of the Vbat can vary between 1V and 6V and it's series resistance can vary between 100 Ohm and 500 Ohm.
    2) Vout of the V_REG block needs to be 2.5V

Using an LDO would not satisfy the efficienty requirement, hence my guess is that some sort of buck/boost solution should be used.

Does anybody have buck/boost chips, combinations of such chips or any other solutions in mind that might suit this problem? 

Basic schematic of the above: