Minty Variational Principle for Nonsmooth Interval-Valued Vector Optimization Problems on Hadamard Manifolds
Savin Treanţă, Priyanka Mishra, Balendu Bhooshan Upadhyay
Abstract
This article deals with the classes of approximate Minty- and Stampacchia-type vector variational inequalities on Hadamard manifolds and a class of nonsmooth interval-valued vector optimization problems. By using the Clarke subdifferentials, we define a new class of functions on Hadamard manifolds, namely, the geodesic LU-approximately convex functions. Under geodesic LU-approximate convexity hypothesis, we derive the relationship between the solutions of these approximate vector variational inequalities and nonsmooth interval-valued vector optimization problems. This paper extends and generalizes some existing results in the literature.
Topics & Concepts
Hadamard transformMathematicsVariational inequalityGeodesicConvexityHadamard three-lines theoremInterval (graph theory)Vector optimizationClass (philosophy)Applied mathematicsPure mathematicsConvex functionRegular polygonMathematical analysisOptimization problemMathematical optimizationHadamard matrixCombinatoricsComputer scienceGeometryEconomicsFinancial economicsMulti-swarm optimizationArtificial intelligenceOptimization and Variational AnalysisContact Mechanics and Variational InequalitiesTopology Optimization in Engineering