title: What is the general name of this vector sum problem?
body: <p>Given the USDA nutrient database: n vectors where each dimension is a particular nutrient, 
  find a set S of foods F whose vectors sum to .ge. RDA and .lt. any toxic value. Add various other constraints to the model, e.g., calories, mass.
  Solve for any combination of vectors that meet the constraints.</p>
  
  <p>Currently available websites allow one to choose foods one at a time and build a "recipe". I'm looking for a computational solution. I suspect that this is a trivial problem that someone has already solved. I am looking for the search terms that describe this sort of scenario.</p>
  
  <p>"Deep learning" looks for patterns, but the goal "pattern" is an input. Probability is not involved, so a sizable chunk of ML is not applicable. I intuit that some sort of tree-traversal might be useful.<br>
  This is a combination of set theory and vector math. I expect that there exists a large solution set of sets.<br>
  I can set up the input vectors as parameterized SQL queries. I have downloaded the USDA nutrient database and loaded it into mariadb.</p>
  
  <p>pseudocode: 
  Select * 
  from subset_nutrients 
  join rda_nutrs on nutrients.nut-1 = rda-nuts.nut-1 join toxicity on nutrients.nut-1 = toxicity.nut-t1<br>
  where sum(nut-1scalar) >= rda-1scalar and sum(nut-2scalar) >=rda-2scalar {etc} and sum(nut-1scalar) &lt; toxicity.nut1_t_scalar and sum(nut-2scalar) &lt; toxicity.nut2_t_scalar {etc}</p>
  
  <p>SQL might actually solve the problem all by itself?</p>
  
  <p>I am looking for human-suggested search terms to find original sources of information. Thank you for your suggestions.</p>