At the local level there are efforts via Preuss School, the Early Academic Outreach Program, and the TRIO Outreach Programs. I'm sure there are more programs but these are the ones I'm familiar with.
At the semi-local/international level (let's face it, there's no San Diego without Tijuana and vice-versa) there's the Center for US-Mexican Studies and those pacts UCSD and UABC have made via this centre.
I don't know what UCSD is doing outside of San Diego/Tijuana. I'm a local so this is as much as I know about UCSD's outreach to minorities. In my opinion there's only so much the university can do. If more minorities don't want to apply or attend, that's a personal decision, which UCSD has no control over. You can't force everyone to want a university education. And you can't force the school to offer admittance to every single applicant of minority status. I say this as a person of minority status who has a lot of family members who think a university education is a joke, a waste of time, or just "not for me." They have many things in their favor but a higher education just doesn't appeal to them for whatever reason. I'm not saying this is the case across the board, but it's what I've seen in my personal bubble.
UCSD is only 20-something% white and I think like 40-something% Asian. UCLA and Berkeley have a similar percentage of white students and a smaller percentage of Asian students, though Asian students make up the majority in both cases. These stats I provided may be a little outdated but I don't think the numbers have dramatically increased or decreased. The UC system has a different breakdown than does the CSU system. For example, Humboldt has a pretty even white vs. Latino ratio (in the 30-something% for both). Some CSUs are largely Latino, like Fullerton or Long Beach. Our neighbor SDSU has a larger white percentage. CalPoly SLO, on the other hand, is largely white in comparison to the other CSUs. I'm already ranting here but, at least as far as the overall minority breakdown is concerned, UC schools are not like other schools. It's a shame that the black population on these campuses is incredibly, incredibly low. And don't even get me started on the Native American population. But, like I said above, I believe there's only so much a university can do to recruit these groups. It all comes down to personal decision. And, yes, many students don't have the resources necessary, or the support necessary, to pursue a university education even if they want to. That's a problem outside of the university's jurisdiction. It's not that easy to cut tuition costs. I wish it would. It would save me a lot of debt that I've accumulated. But there are a lot of factors at play.
Anyway, my two cents. I don't have an answer to OP's question.