Continuous Optimisation HT26, Convex optimality conditions

Created: January 22, 2026 | Updated: January 22, 2026 | About these notes | View in context | Study these flashcards

---

• [[Course - Continuous Optimisation HT26]]^U
  • See also:
  • [[Notes - Machine Learning MT23, Convex optimisation]]^U
  • [[Notes - Optimisation for Data Science HT25, Smoothness and convexity]]^U

Flashcards

@State a necessary and sufficient condition for $f \in \mathcal C^2(\mathbb R^n)$ function to be convex.

---

\[\nabla^2 f(x) \succeq 0\]

for all $x \in \mathbb R^n$.

---

Related posts

• [[Course - Continuous Optimisation HT26]]^U

  (outgoing)
• [[Notes - Continuous Optimisation HT26, Unconstrained optimality conditions]]^U

  (sim: 0.732)
• [[Notes - Continuous Optimisation HT26, Taylor's theorem]]^U

  (sim: 0.665)
• [[Notes - Optimisation for Data Science HT25, Subgradients]]^U

  (sim: 0.673)
• [[Notes - Optimisation for Data Science HT25, Smoothness and convexity]]^U

  (outgoing)
• [[Notes - Machine Learning MT23, Convex optimisation]]^U

  (outgoing)
• [[Lecture - Continuous Mathematics HT23, VI]]^U

  (sim: 0.671)