On Debreu-Koopmans theorem for additively decomposed quasiconvex functions Event

Time:

11:00 - 12:00

Date:

2026-09-10 16:27:00

Venue:

Ketley Room B54/4001

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Event details

The Debreu–Koopmans theorem [1] shows that if a separable function

h(x₁, …, xₙ) = ∑ⁿᵢ₌₁ hᵢ(xᵢ),

is quasiconvex, then at most one hᵢ might be nonconvex and, as a consequence, when all components hᵢ are quasiconvex, h is not quasiconvex and it is not known to which class of functions h belongs, giving rise to the Debreu–Koopmans problem.

In this talk, we introduce the class of (strongly) star quasiconvex functions [4], and we prove that h is (strongly) star quasiconvex if and only if all components hᵢ are (strongly) star quasiconvex [2] and, as a consequence, we solves the Debreu–Koopmans problem. This result has strong implications in economic theory, since formally bridges classical diversification theory with behavioural economics, as it implies that separable S-shaped (Sigmoid) value/utility functions from Prospect Theory [3] are star quasiconvex. 

Finally, and if the time allows us, we present potential applications in economics and further research directions.

[1] G. Debreu, T.C. Koopmans, Additively decomposed quasiconvex functions, Math. Programm., 24, pp. 1–38, 1982.

[2] F. Lara, On Debreu–Koopmans theorem for additively decomposed quasiconvex functions with applications, arXiv: 2603.17088, 2026.

[3] D. Kahneman, A. Tversky, Prospect theory: an analysis of decision under risk, Econometrica, 47, (2), pp. 263–292, 1979.

[4] P.Q. Khanh, F. Lara, Star quasiconvexity: a unified approach for linear convergence of first-order methods beyond convexity, arXiv: 2510.24981, 2025.

About the Speaker

Felipe Lara is a Full Professor of Optimization at the Instituto de Alta Investigación, Universidad de Tarapacá, in Arica, Chile. He obtained his Ph.D. degree from the Universidad de Concepción, Chile, in 2015, under the joint supervision of Fabián Flores-Bazán and Nicolas Hadjisavvas. He has authored more than 50 ISI/WOS-indexed papers, 9 of which are single-authored, and currently serves as Associate Editor for the journals Optimization and Journal of Optimization Theory and Applications. His research interests focus primarly on on generalized convexity and generalized monotonicity, first-order algorithms, equilibrium problems and economic applications.