Minimizing Nonconvex, Simple Integrals of Product Type

The full text article is not available for purchase.

The publisher only permits individual articles to be downloaded by subscribers.


We consider the problem of minimizing simple integrals of product type, i.e. min ∫T0 g(x(t)) f(x′(t)) dt: xAC([0, T]), x(0)=x0,  x(T)=xT,where f:ℝ→[0, ∞] is a possibly nonconvex, lower semicontinuous function with either superlinear or slow growth at infinity. Assuming that the relaxed problem (**) obtained from () by replacing f with its convex envelope f** admits a solution, we prove attainment for () for every continuous, positively bounded below the coefficient g such that (i) every point t∈ℝ is squeezed between two intervals where g is monotone and (ii) g has no strict local minima. This shows in particular that, for those f such that the relaxed problem (**) has a solution, the class of coefficients g that yield existence to () is dense in the space of continuous, positive functions on ℝ. We discuss various instances of growth conditions on f that yield solutions to (**) and we present examples that show that the hypotheses on g considered above for attainment are essentially sharp. Copyright 2001 Academic Press.

Keywords: existence of solutions; nonconvex minimum problems; simple integrals

Document Type: Research Article

Affiliations: 1: Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, P.le Europa 1, Trieste, I-34127, Italy 2: Dipartimento di Matematica Pura ed Applicata “G. Vitali”, Università degli Studi di Modena e Reggio Emilia, Via Campi 213/B, Modena, I-41100, Italy

Publication date: March 1, 2001

Related content



Share Content

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more