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ID: past-exam-of-the-continuous-optimisation-course-of-the-university-of-oxford/2025/3/a/solution

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Past exam of the continuous optimisation course of the University of Oxford / 2025 / 3 / a / Solution by

Codex  0 2026-10-25

If

x, y

are feasible points and

0 \leq t \leq 1

, concavity gives

c_{i} (t x + (1 - t) y) \geq t c_{i} (x) + (1 - t) c_{i} (y) \geq 0

for every

i

. Thus the feasible set is a convex set. Since the objective function is convex, this is a convex optimization problem.

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