This paper is devoted to a discussion of the use of nonlinear multiobjective models for the analysis of environmental policy. The central focus of the paper is on an interactive procedure by way of a so-called displaced ideal approach. The conflicting nature of multiple objectives in a spatial and environmental system is analyzed by means of a spatial variant of the ‘keeping up with the Joneses' effect.
Geometric programming appears to be a useful tool to solve these nonlinear spatial—environmental multiobjective models.
DinkelJ JKochenbergerG AMcCarlB, 1974“An approach to the numerical solution of geometric programs”Mathematical Programming7181–190
3.
DuesenberryJ S, 1952Income, Saving and the Theory of Consumer Behaviour (Harvard University Press, Cambridge, Mass)
4.
DuffinR JPetersonE LZenerC M, 1967Geometric Programming (John Wiley, New York)
5.
DuffinR JPetersonE L, 1973“Geometric programming with signomials”Journal of Optimization Theory and Applications113–35
6.
GeoffrionA M, 1967“Solving bicriterion mathematical programs”Operations Research15(1) 39–54
7.
GeoffrionA M, 1968“Proper efficiency and the theory of vector maximization”Journal of Mathematical Analysis and Applications22618–630
8.
HafkampWNijkampP, 1979“Environmental protection and spatial welfare patterns” in Spatial Inequalities and Regional Development Eds FolmerHOosterhavenJ (Martinus Nijhoff, Leiden) pp 47–92
9.
HardyG HLittlewoodJ FPolyaG, 1959Inequalities (Cambridge University Press, London)
10.
KlaassenL H, 1978“De nota inzake het regionale sociaal-economische beleid 1977 t/m 1980” in Regional Beleid Eds NijkampPVerhageC (Martinus Nijhoff, Leiden) pp 43–52
11.
KuhnH WTuckerA W, 1968“Nonlinear programming” in Readings in Mathematical Economics Ed. NewmanP (Johns Hopkins University Press, Baltimore, Md) pp 3–14
12.
LeibensteinH, 1976Beyond Economic Man (Harvard University Press, Cambridge, Mass)
13.
LuptácikM, 1977Geometrische Programmierung und Ökonomische Analyse (Anton Hain, Meisenheim am Glan, BRD)
14.
NijkampP, 1972Planning of Industrial Complexes by Means of Geometric Programming (Nijgh and Van Ditmar, The Hague)
15.
NijkampP, 1977aTheory and Application of Environmental Economics (North-Holland, Amsterdam)
16.
NijkampP, 1977b“New decision models for multiple goals” Research Memorandum 69, Department of Economics, Free University, Amsterdam
17.
NijkampPSomermeijerW H, 1971“Explicating implicit social preference functions”Economics of Planning11(3) 100–119
18.
PaelinckJ H PNijkampP, 1976Operational Theory and Method of Regional Economics (Saxon House, Teakfield, Farnborough, Hants)
19.
PascualL DBen-IsraelA, 1971“Vector-valued criteria in geometric programming”Operations Research19(1) 98–104
RijckaertM G, 1977“Computational aspects of geometric programming”Department of Operations Research, Catholic University of Louvain, Louvain, Belgium (mimeo)
22.
Van DelftANijkampP, 1977Multi-criteria Analysis and Regional Decision-making (Martinus Nijhoff, Leiden)
23.
VemuriV, 1974“Multiple-objective optimization in water resource systems”Water Resources Research10(1) 44–48
24.
ZangwillW I, 1969Nonlinear Programming: A Unified Approach (Prentice-Hall, Englewood Cliffs, NJ)
25.
ZelenyM, 1976“The theory of displaced ideal” in Multiple Criteria Decision Making Ed. ZelenyM (Springer, Berlin) pp 153–206
