system
Given the following post, respond as if you're commenting on Reddit:
human
[Half-Life] How did HECU's objectives change over the course of the Black Mesa incident?
gpt
The HECU's initial orders were to eliminate the extra-dimensional invaders, as well as the science and security personnel within the Black Mesa compound.  This would ensure that Black Mesa would remain a viable and valuable research center, while also covering up the Resonance Cascade incident by eliminating all witnesses.  

However, the HECU found themselves overwhelmed by the opposition they faced.  The creatures that teleported into the Black Mesa facility were tougher and more numerous than the HECU had expected.  Previously, humanity's experience with these alien creatures were limited to the likes of Headcrabs and Houndeyes.  Now the HECU were dealing with the likes of Vortigaunts, Grunts, Gargantuas, etc.  Additionally, resistance from the science and security personnel was greater than expected.  In particular, one Black Mesa researcher known as Gordon Freeman was able to kill and evade HECU troops almost at will.  

The HECU tried to respond by bringing in greater force against their enemies.  For example, they flew in greater numbers of troops, deploying them quickly by having their soldiers rappel down from transport aircraft, such as Ospreys.  In addition, the HECU also called in artillery strikes and air strikes.  Finally, they also recognized the danger that Gordon Freeman represented, and targeted him specifically.  However, despite these measures, the HECU were still unable to turn the tide of the battle.  

As a result of suffering significant losses, the HECU began pulling out of Black Mesa. Their objective had changed from cleanup to cutting their losses.  As a result of the HECU's failure, a large Black Ops team was sent in.  The Black Ops team had four objectives.  The first two, eliminate the aliens and eliminate the human personnel, were the same as the HECU's goals.  The other two, however, were not.  The Black Ops were to eliminate any HECU soldiers they encountered (again, to get rid of witnesses), and in addition the Black Ops set up a nuclear warhead to detonate and destroy the entire Black Mesa facility.  

The attack by the Black Ops took the HECU by surprise.  As a result, the Black Ops were very successful in their mission to eliminate HECU members.  

So, to summarize, the HECU's objectives were initially to destroy the alien invaders and silence all witnesses.  When this proved more difficult than they'd anticipated, the HECU escalated.  Then, after realizing they couldn't win, the HECU's objective became one of retreat and withdrawal.  Finally, when the Black Ops arrived and started attacking the HECU soldiers, the HECU's scattered forces still in Black Mesa only had one possible objective left:  survive.