A Derivative-Free Trust-Region Method for Biobjective Optimization

Ryu, Jong-hyun; Kim, Sujin

doi:10.1137/120864738

Cited by 33 publications

(34 citation statements)

References 15 publications

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“…Another approach on which derivative-free methods are based on is the trust region method [6,7,8,9,10]. There are also multiobjective realizations of this approach [29,36]. Trust region methods are not initially designed for expensive functions but can easily be adapted to them.…”

Section: Introductionmentioning

confidence: 99%

A Trust-Region Algorithm for Heterogeneous Multiobjective Optimization

Thomann¹,

Eichfelder²

2019

SIAM J. Optim.

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This paper presents a new trust region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, for example given by a time-consuming simulation. For this function derivative information cannot be used and the computation of function values involves high computational effort. The other objective functions are given analytically and derivatives can easily be computed. The method uses the basic trust region approach by restricting the computations in every iteration to a local area and replacing the objective functions by suitable models. The search direction is generated in the image space by using local ideal points. It is proved that the presented algorithm converges to a Pareto critical point. Numerical results are presented and compared to another algorithm. Mathematics subject classifications (MSC2010): 90C29, 90C56, 90C30 * This work was funded by DFG under no. GRK 1567.

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Section: Introductionmentioning

confidence: 99%

A Trust-Region Algorithm for Heterogeneous Multiobjective Optimization

Thomann¹,

Eichfelder²

2019

SIAM J. Optim.

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“…The simplex method of Rykov [1980] includes ideas from model-based methods. Rykov varies the number of reflected vertices from iteration to iteration, following one of three rules that depend on…”

Section: Simplex Methodsmentioning

confidence: 99%

Derivative-free optimization methods

2019

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Dedicated to the memory of Andrew R. Conn for his inspiring enthusiasm and his many contributions to the renaissance of derivative-free optimization methods. AbstractIn many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.

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“…In this case, the trial point provides a descent for every objective function. This realization of the trial point acceptance test is for example used in [16] and it is stricter than the trial point acceptance test used in MHT: Lem. 4.23] Let k ∈ N be an arbitrary index, η 1 ∈ (0, 1) a constant and let Assumption A.4 hold.…”

Section: Step 3: Trial Point Acceptance Testmentioning

confidence: 99%

Representation of the Pareto front for heterogeneous multi-objective optimization

2019

J. Appl. Numer. Optim.

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Optimization problems with multiple objectives which are expensive, i. e., where function evaluations are time consuming, are difficult to solve. Finding at least one locally optimal solution is already a difficult task. In case only one of the objective functions is expensive while the others are cheap, for instance, analytically given, this can be used in the optimization procedure. Using a trust-region approach and the Tammer-Weidner-functional for finding descent directions, in [19] an algorithm was proposed which makes use of the heterogeneity of the objective functions. In this paper, we present three heuristic approaches, which allow to find additional optimal solutions of the multiobjective optimization problem and by that representations at least of parts of the Pareto front. We present the related theoretical results as well as numerical results on some test instances.

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A Derivative-Free Trust-Region Method for Biobjective Optimization

Cited by 33 publications

References 15 publications

A Trust-Region Algorithm for Heterogeneous Multiobjective Optimization

A Trust-Region Algorithm for Heterogeneous Multiobjective Optimization

Derivative-free optimization methods

Representation of the Pareto front for heterogeneous multi-objective optimization

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