Dynamic soliton–mean flow interaction with non-convex flux

Provable Non-convex Phase Retrieval with Outliers: Median TruncatedWirtinger Flow

Solving systems of quadratic equations is a central problem in machine learning and signal processing. One important example is phase retrieval, which aims to recover a signal from only magnitudes of its linear measurements. This paper focuses on the situation when the measurements are corrupted by arbitrary outliers, for which the recently developed non-convex gradient descent Wirtinger flow (...

Non-convex dynamic programming and optimal investment

We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal portfolios for non-concave utility maximization problems in financial market models with frictions (such as illiquidity), a first result of its kind. The proofs are based...

Non convex technologies and economic efficiency measure with imprecise data

The Semigroup Generated by a Temple Class System with Non–convex Flux Function

We consider the Cauchy problem for a nonlinear n × n system of conservation laws of Temple class, i.e. with coinciding shock and rarefaction curves and with a coordinate system made of Riemann invariants. Without any assumption on the convexity of the flux function, we prove the existence of a semigroup made of weak solutions of the equations and depending Lipschitz continuously on the initial ...

Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux. I

We discuss different notions of continuous solutions to the balance law ∂tu + ∂x(f(u)) = g with g bounded and f ∈ C, extending previous works relative to the flux f(u) = u. We establish the equivalence among distributional solutions and a suitable notion of Lagrangian solutions for general smooth fluxes. We eventually find that continuous solutions are Kružkov iso-entropy solutions, which yield...