Is it true that running a halogen light bulb at less than 100% brightness actually shortens its life due to the inability of the halogen cycle to occur?  Would running one of my BT15 Philips halogens pictured below at about 50% brightness shorten its long 3000 hour life?

When reducing the temperature even a bit, the halogen cycle would become unnecessary in the first place, so the eventual stopping of the cycle would not harm the lamp at all.

But there is another problem:
When the filament becomes too cold, the halogens may start to attack it. And that may really reduce the lamp life. This may happen on really low temperatures, when the tungsten is still dark, so in real life this won't happen for the main filament at all. Don't forget there are many tungsten halogen IR heat lamps with rated life in high 10k hours rated life.
The problem, however, could be the lead wires entering the bulb. These section normally run way cooler than the rest of the filament and so are likely to operate at low enough temperature for the halogens to attack it. The heat lamps do not suffer from this, as they are thermally designed so the lead in sections are relatively (to the main filament part; compare to the lighting service lamps) hotter, but underdriving any halogen too much may pose such problem. The result is then the filament breaking off from the lamp ends, otherwise looking intact.

I've seen quite a few installation of linear halogens operated just plain via a diode (so 50% power i.e. 70% voltage) 16hours/day many years in a row, so for sure way longer than their life rating (a mood lighting in a restaurant). So apparently in that case the heat related filament degradation was slowed down way more significantly than the problems with the attacking halogens. But that could be really specific for certain lamp make and model. It well may be, other make or model lamp may last shorter than rated, just because of a different internal thermal design.

Hey Medved, I see that you mentioned cold conditions being harmful for the filament in a halogen bulb.  I have a floodlight on the outside of my house with a T3 halogen bulb in it.  Does that mean that cold winter temperatures outside make the filament become brittle?  I think thermal shock would be a problem too, if I flipped the 300 watt lamp on during a cold day.  The halogen gases would be under attack during the cold environmental temperatures and that explains why this halogen lamp has had to be replaced a few times despite not being used frequently.

The lamp design must be so, that at full power the Halogens won't neck the filament. I think this definitely calls for some safety margin, so with all possible lamp to lamp variations, line voltage etc, guarantee that necking won't become a problem. Assuming our lamp isnt allready marginal in its make, and our line voltage isnt allready marginally low, then there is still more margin to dim the lamp into without running into necking

On the other hand we know, that even the slightest dimming have very significant positive effect on the main filament life

So what i conclude, is that around the full power point, d(power)/d(life) is negative i.e. dimming will improve lamp life. How far this area extends ? Dont know, but i'd think on the order of 10's %s

Interesting.  It makes sense that a 60 watt halogen lamp running at 30 watts will last longer in terms of the filament not burning as intensely.  Of course, voltage spikes or other kinds of unlikely power surges will undermine the positive effects of dimming.

Hey Medved, I see that you mentioned cold conditions being harmful for the filament in a halogen bulb.  I have a floodlight on the outside of my house with a T3 halogen bulb in it.  Does that mean that cold winter temperatures outside make the filament become brittle?  I think thermal shock would be a problem too, if I flipped the 300 watt lamp on during a cold day.  The halogen gases would be under attack during the cold environmental temperatures and that explains why this halogen lamp has had to be replaced a few times despite not being used frequently.

It is not abot external temperatures, these may vary between -40degC (probably the coldest inhabitated regions) to 60degC (the hottest parts), what is barely 100degC difference.
What matters is, if the coldest part of the filament runs below (ball park) 500degC or above 1000degC (difference caused by just dimming to 50% power). So the external temperature wont have any observable effect at all.

For filaments getting brittle, the danger comes from other direction: When turned ON cold at full voltage, the filament has very low resistance and so pass high current. At that moment no problem. But when the warmup uniformity is not perfect, some parts of the filament warm up way faster, these sections then have higher resistance than the rest, so concentrate the power dissipation, further worsening the differences. These nonuniformities  then cause some sections of the filament to briefly reach temperatures significantly above to what the lamp is designed for (just for brief moment, when the other sections reach the full temperature, the overcurrent disappears and so the temperature goes back). Because halogens are designed to operate at really high temperatures, even the little extra causes the temperature to cross the recrystalization  threshold, the tungsten changes structure there, usually becomes more brittle. And next time the effect will be even worse, as that changed region tends to be more resistive.
This is a major degradation mechanism for mainly low power (100W and below), high voltage (mains) lamps. And it forces the lamp designers to operate the filament a bit colder, so loose the efficacy compare to e.g. the 12V halogens.
For that any form of reduced power during start will help a lot - it give time for the filament temperature to better even out, so prevents reaching the recrystalization temperatures.

I once had a touch pad dimmer that any lamp could plug into.  This dimmer used a "slow start" for incandescent or halogen bulbs that lit them gradually in about a second instead of instantly turning them on like most light switches.  The more gradual temperature change when powered on lead to longer bulb life and less stress on the filament.