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Glite Dictionary
🔍 Convex both sides 📈 Convex in variables
biconvex

biconvex

9.7
In math, a function that is convex in each variable when other variables are fixed
  • adjective
  • /ˌbaɪkənˈvɛks/
  • Specialized
translation icon : biconvexo
  • A function is biconvex if it is convex in each variable.

Examples

  • They proved the function f(x,y) is biconvex for fixed y and for fixed x separately.

  • The optimization problem was biconvex, so alternating minimization often finds a good solution.

  • A biconvex cost model allows alternating optimization to converge quickly in many cases.

  • The optimization problem is biconvex in nature.

  • The function is biconvex when considering its behavior in each dimension separately.

  • In their research, they demonstrated that the cost function is biconvex under certain conditions.

  • For optimization algorithms to work efficiently, the problem must be biconvex when fixing different variables.

Surface Forms

biconvex positive

Morphology

biconvex = convex (semi-transparent) = bi + convex

Morphologically clear ('bi-' + 'convex'), but the mathematical sense (convex in each variable separately) is a technical extension that a general learner may not infer.

Etymology

The word biconvex also uses bi- meaning 'two', as in bicycle, and convex meaning 'no dips', so in math a biconvex problem is 'convex' in each part when the other part is fixed, and that is why simple methods that change one part at a time often find a good solution.