A class of adaptive algorithms for approximating convex bodies by polyhedra
Computational Mathematics and Mathematical Physics
Analysis of an algorithm for approximating convex bodies
Computational Mathematics and Mathematical Physics
Norm-Based Approximation in Bicriteria Programming
Computational Optimization and Applications
Model-Based Decision Support Methodology with Environmental Applications
Model-Based Decision Support Methodology with Environmental Applications
Introducing oblique norms into multiple criteria programming
Journal of Global Optimization
Convex Optimization
On min-norm and min-max methods of multi-objective optimization
Mathematical Programming: Series A and B
Multicriteria Optimization
Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software
Finding representative systems for discrete bicriterion optimization problems
Operations Research Letters
Greedy algorithms for a class of knapsack problems with binary weights
Computers and Operations Research
Finding Efficient Solutions by Free Disposal Outer Approximation
SIAM Journal on Optimization
Multimodal optimization using a bi-objective evolutionary algorithm
Evolutionary Computation
Adaptive MOEA/D for QoS-based web service composition
EvoCOP'13 Proceedings of the 13th European conference on Evolutionary Computation in Combinatorial Optimization
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In practical applications of mathematical programming it is frequently observed that the decision maker prefers apparently suboptimal solutions. A natural explanation for this phenomenon is that the applied mathematical model was not sufficiently realistic and did not fully represent all the decision makers criteria and constraints. Since multicriteria optimization approaches are specifically designed to incorporate such complex preference structures, they gain more and more importance in application areas as, for example, engineering design and capital budgeting. The aim of this paper is to analyze optimization problems both from a constrained programming and a multicriteria programming perspective. It is shown that both formulations share important properties, and that many classical solution approaches have correspondences in the respective models. The analysis naturally leads to a discussion of the applicability of some recent approximation techniques for multicriteria programming problems for the approximation of optimal solutions and of Lagrange multipliers in convex constrained programming. Convergence results are proven for convex and nonconvex problems.