Multibundle Method for Constrained Nonsmooth Multiobjective DC Optimization
Springer
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In this paper, we MultibundleOptimizationpropose a multibundleMultibundle method. The new method is of the descent type and it is designedDesign for constrained nonsmooth multiobjective optimizationOptimization problemsProblem whose objectives and constraints can be represented as a difference of convex (DC) functionsFunction. The method combines pieces from the multiple subgradientGradient descent bundle method [49], the double bundle method [26], and the multiobjective double bundle method [47]. The idea is to find descent directions for every individual objective by using a single-objective bundle method designedDesign for DC functionsFunction, and then, form a common descent direction. The novelty in our approach is that the decision maker has an option to steer the solutionSolution process by indicating whether an individual descent direction should be used to improve one objective or should the method test the optimality. Furthermore, we present two alternative constraint handling strategies. The multibundle method is proven to have a finite convergenceConvergence to an approximate weakly Pareto stationary solutionSolution under mild assumptions. Finally, the new method is compared with a multiobjective DC method as well as a multiobjective nonconvex method to demonstrate the numericalNumerical capability of the proposed method. In addition, the constraint handling strategies are compared and some interactive examples are given.
Sarja
Computational Methods in Applied Sciences