Book Chapter10.1007/0-306-48107-3_2
Nonlinear Multiobjective Programming
Tetsuzo Tanino,Hun Kuk +1 more
- 01 Jan 2003
- pp 71-128
19
TL;DR: In this paper, the authors provide an annotated bibliography of nonlinear multiobjective programming problems, including scalarization techniques and optimality conditions for nonlinear MOP problems.
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Abstract: This chapter provides an annotated bibliography of nonlinear multiobjective programming. The list of references comprises more than 500 entries. First we explain some solution concepts which are fundamental and important in multiobjective optimization. Some basic properties of the solution sets are also discussed. The next section is devoted to scalarization techniques and optimality conditions for nonlinear multiobjective programming problems. The third topic is stability and sensitivity analysis, which discusses the behavior of the set of efficient points according to the change of parameter values in a nonlinear multiobjective programming problem qualitatively and quantitatively. The following section is devoted to several aspects of duality theory, i.e., Lagrange duality, conjugate duality and Wolfe type and Mond-Weir type duality with generalized convexity. Finally vector variational inequalities are also dealt with.
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Citations
Designing safe drug names.
TL;DR: This paper attempts to lay out a systematic approach to the design of safe drug names by characterising the process of design as a multiple-objective optimisation problem, and describes several approaches to selecting one design from a set of competing alternatives.
57
Stability for Properly Quasiconvex Vector Optimization Problem
TL;DR: The Kuratowski–Painlevé set-convergence of the sets of minimal, weak minimal and Henig proper minimal points of the perturbed problems to the corresponding minimal set of the original problem is established assuming the objective functions to be (strictly) properly quasi cone-convex.
25
A general approach for studying duality in multiobjective optimization
TL;DR: A general duality framework in convex multiobjective optimization is established using the scalarization with K-strongly increasing functions and the conjugate duality for composed convex cone-constrained optimization problems.
Stability results for convex vector-valued optimization problems
TL;DR: In this paper, the authors discuss the stability of the sets of efficient points of vector-valued optimization problems when the data of the approximate problems converges to the original problem in the sense of Painleve-Kuratowski.
19
Extended compact genetic algorithm applied for optimum allocation of power quality monitors in transmission systems
Hermes Manoel Galvão Castelo Branco,R. P. da Silva,Mario Oleskovicz,Denis Vinicius Coury,Alexandre C. B. Delbem +4 more
- 24 Jul 2011
TL;DR: In this article, a methodology for solving optimum allocation of power quality monitors in transmission power systems is presented, where the problem is modeled as a multi-objective problem to acquire the lowest cost solution with the highest data redundancy.
7
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TL;DR: The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.
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Nonlinear Multiobjective Optimization
Kaisa Miettinen
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Multiple Criteria Optimization: Theory, Computation, and Application
R. S. Laundy
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TL;DR: Mathematical Background Topics from Linear Algebra Single Objective Linear Programming Determining all Alternative Optima Comments about Objective Row Parametric Programming Utility Functions, Nondominated Criterion Vectors and Efficient Points Point Estimate Weighted-sums Approach.
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Multiobjective Decision Making: Theory and Methodology
Vira Chankong,Yacov Y. Haimes +1 more
- 01 Jan 1983
2.6K
Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems
Indraneel Das,John E. Dennis +1 more
TL;DR: In this paper, an alternate method for finding several Pareto optimal points for a general nonlinear multicriteria optimization problem is proposed, which can handle more than two objectives while retaining the computational efficiency of continuation-type algorithms.