Optimization over the efficient set

DOI10.1016/0022-247X(84)90269-5zbMath0534.90077MaRDI QIDQ5896268

Harold P. Benson

Publication date: 1984

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

optimal solutionsefficient solutionunboundedness conditionsvector maximization

Mathematics Subject Classification ID

Sensitivity, stability, parametric optimization (90C31)

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Cites Work

• Unnamed Item
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• Efficiency and proper efficiency in vector maximization with respect to cones
• An improved definition of proper efficiency for vector maximization with respect to cones
• Proper efficiency with respect to cones
• The set of all nondominated solutions in linear cases and a multicriteria simplex method
• Linear multiobjective programming
• Connectedness of the set of nondominated outcomes in multicriteria optimization
• A general method for determining the set of all efficient solutions to a linear vectormaximum problem
• Existence of efficient solutions for vector maximization problems
• A survey of multicriteria optimization or the vector maximum problem. I: 1776-1960
• The structure of admissible points with respect to cone dominance
• Generating all maximal efficient faces for multiple objective linear programs
• A finite, nonadjacent extreme-point search algorithm for optimization over the efficient set
• Proper efficiency and the theory of vector maximization
• Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
• Global Maximization of a Convex Function with Linear Inequality Constraints
• An algorithm for nonconvex programming problems
• A cutting plane algorithm for solving bilinear programs
• The Vector Maximization Problem: Proper Efficiency and Stability
• A Successive Underestimation Method for Concave Minimization Problems
• Bilinear programming: An exact algorithm
• Proper Efficient Points for Maximizations with Respect to Cones
• The Enumeration of the Set of All Efficient Solutions for a Linear Multiple Objective Program
• On Cone-Efficiency, Cone-Convexity and Cone-Compactness
• Finding all efficient extreme points for multiple objective linear programs
• On a property of polyhedral sets
• A revised simplex method for linear multiple objective programs
• Algorithms for the vector maximization problem