iS this possible? F output > F input?
F output = force generated due to the displacement of piston magnet
F input = force required to move the shield away from the piston magnet.

1-there should be and input force F input acting on the shield in the direction of the shield movement. 
2- when the shield shift away from the piston magnet repulsion forces noted creating an outPut work.
3- the small neo magnets have a weaker and short magnetic field range creating repulsion zone when other magnets are in close proximity to the shield.
4- the shield in very close proximity to Neo magnets generates repulsion field to neutralize The attraction drag force. however, there will be an attraction drag force noted above the neutral zone from piston magnet as it moves away.  the attraction force from the attraction zone will be substantially weaker as the force is inversely proportional to distance.
5- the edges of the shield have triangular shape to reduce the surface area of attraction
6- since the shield is hovering on A track Of fixed magnets the shield experience A uniform symmetrical force distribution therefore no drug is noted from below.  the only drag force Imposed on the shield is from the piston magnet.

Hi Superhero,

iS this possible? F output > F input?
F output = force generated due to the displacement of piston magnet
F input = force required to move the shield away from the piston magnet.

There is an interesting Chinese patent that shows that it's "possible" to extend equal force over time but the force generated is equivalent so it won't run itself.

https://www.google.com/patents/CN1153422A?cl=en

You are correct involving any shield will always consume any gain operating the shield due to drag and friction.  it is possible to eliminate friction and minimize drag with a unique design as proposed in the document 137.pdf above.  friction could be eliminated by utilizing both attraction and repulsion in the shield to create a hover like effect.  As to drag the shape of the shield plays a big role in reducing it. perhaps instead of trianglar shape as shown above a cone shape edges could be more beneficial, to reduce the surface area when the shield is shifting.  Also, the timing of the input force is very important, it must be Introduced  exactly at the shifting instant when shield is under piston magnet.
Please download it for further clarification.

I have already built the device in the Chinese patent and also a circular rotary device operating on the same principal just to be certain of the outcome.
The results are negative on both devices though the rotary device does provide some interesting gearing effect but of little value.

The fact remains that moving a magnet from behind a shield into repulsion with another magnet causes a much greater attraction to the shield than when the repulsing magnet is not there.

Also when moving a magnet into a shield from another attracting magnet, there is less attraction to the shield than when the attracting magnet is not present.

So from this one can conclude that the use of a shield has no positive value in any attempt of energy gain. As was expected.

I am convinced that it's impossible to get an energy gain from magnetic fields whether electrically generated or permanent magnet.

Not to say that it is forever impossible because some new material may be developed with properties that might provide some OU effect.