What's $argmax$ in multiobjective optimization? Is it component-wise or something else?

Question

Such as in the weighting method:

$$\sum_{i=1}^n w_i p_i$$

then what is

$$argmax_p\sum_{i=1}^n w_i p_i$$

Is it the $p$ that produces the largest sum? Or that has some kind of component-wise dominance?

@YuvalFilmus But this example comes from a course in multiobjective optimization. — mavavilj, Apr 06 '19 at 12:06
Nevertheless, it has a single objective, namely $\sum_{i=1}^n w_i p_i$. — Yuval Filmus, Apr 06 '19 at 12:10

score 1 · Answer 1 · answered Apr 06 '19 at 12:09

1

$max\{f(x)\}$ is the maximum value the function assumes, while $argmax\{f(x)\}$ is the value of the $x$ on which the function $f$ assumes the maximum value. The first is in the codomain and the latter in the domain

answered Apr 06 '19 at 12:09

karlabos

1,257

score 0 · Answer 2 · answered Apr 06 '19 at 12:04

0

It is the value of $p_1,\ldots,p_n$ (possibly under some constraints) that maximizes $\sum_{i=1}^n w_i p_i$.

answered Apr 06 '19 at 12:04

Yuval Filmus

57,157

What's $argmax$ in multiobjective optimization? Is it component-wise or something else?

2 Answers2