Saddle-point optimality criteria involving (p, b, d)-invexity and (p, b, d)-pseudoinvexity in interval-valued optimisation problems

ABSTRACT

In this paper, under new generalised convexity assumptions, we investigate some connections between an LU-optimal solution of a variational control problem governed by interval-valued multiple integral functional and a saddle-point associated with an LU-Lagrange functional corresponding to a modified interval-valued variational control problem. Also, in order to illustrate the main results and their effectiveness, we present an application that optimises the mass of a flat plate with interval-valued density that depends on the current point.

Keywords:

• Interval-valued variational control problem
• LU-optimal solution
• saddle-point optimality criteria
• $(\rho ,b,d)$-invexity
• $(\rho ,b,d)$-pseudoinvexity

AMS subject classifications:

• 26B25
• 65K10
• 90C26
• 90C30

Disclosure statement

No potential conflict of interest was reported by the author(s).