Search results for "Bundle method"

showing 3 items of 3 documents

On the methods of nonsmooth optimization

2005

In this paper we shall give a short derivation of the most promising methods in nonsmooth optimization, namely bundle methods. We introduce the basic bundle idea due to Lemarechal and several modifications by Kiwiel, Schramm and Zowe. To the end we shall give some numerical results comparing the efficience of these methods. As test problems we have used well-known test problems from litterature and in addition we shall give some contributions to nonsmooth optimal control problems.

Bundle methodBundleApplied mathematicsDescent directionOptimal controlBundle methodsMathematics
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Branch-and-Bound

2010

We now turn to the discussion of how to solve the linear ordering problem to (proven) optimality. In this chapter we start with the branch-and-bound method which is a general procedure for solving combinatorial optimization problems. In the subsequent chapters this approach will be realized in a special way leading to the so-called branch-and-cut method. There are further possibilities for solving the LOP exactly, e.g. by formulating it as dynamic program or as quadratic assignment problem, but these approaches did not lead to the implementation of practical algorithms and we will not elaborate on them here.

Mathematical optimizationsymbols.namesakeBranch and boundBundle methodQuadratic assignment problemComputer scienceLagrangian relaxationCombinatorial optimization problemsymbolsLinear ordering
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NIMBUS — Interactive Method for Nondifferentiable Multiobjective Optimization Problems

1996

An interactive method, NIMBUS, for nondifferentiable multiobjective optimization problems is introduced. We assume that every objective function is to be minimized The idea of NIMBUS is that the decision maker can easily indicate what kind of improvements are desired and what kind of impairments are tolerable at the point considered.

Multiobjective optimization problemMathematical optimizationPoint (geometry)Decision makerBundle methodsMulti-objective optimizationMathematics
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