Mathematical programs with equilibrium constraints: automatic reformulation and solution via constrained optimization

Constrained optimization has been extensively used to solve many large scale deterministic problems arising in economics, including, for example, square systems of equations and nonlinear programs. A separate set of models have been generated more recently, using complementarity to model various phenomenon, particularly in general equilibria. The unifying framework of mathematical programs with equilibrium constraints (MPEC) has been postulated for problems that combine facets of optimization and complementarity. This paper briefly reviews some methods available to solve these problems and described a new suite of tools for working with MPEC models. Computational results demonstrating the potential of this tool are given that automatically construct and solve a variety of different nonlinear programming reformulations of MPEC problems.\ud \ud This material is based on research partially supported by the National Science Foundation Grant CCR-9972372, the Air Force Office of Scientific Research Grant F49620-01-1-0040, Microsoft Corporation and the Guggenheim Foundation

Effecten van brand op bodem en vegetatie in dennenbossen van voedselarme zandgronden bij Kootwijk

Door atmosferische stikstofdepositie zijn veel bossen van de arme zandgronden vermest en in hun verdere successie verstoord. In een voedselarm dennenbos op zandgrond is onderzocht of door brand de overmaat aan stikstof die in de strooisellaag ligt opgeslagen kan worden teruggedrongen en de bosontwikkeling kan worden teruggezet naar een voedselarme pionierfase. Het onderzoek werd uitgevoerd bij Kootwijk waar in 1995 een bosbrand woedde. De vegetatie- en bodemkundige toestand van voor de brand, één en negen jaar na de brand werd geanalyseerd. Een belangrijke conclusie is dat brand eerder tot een verrijking van de bodem leidt dan tot een verschraling. Door brand vindt een verplaatsing van elementen van ectorganische naar endorganische horizonten plaats. Weliswaar verdwijnt er in zijn totaliteit stikstof, maar direct na de brand is de bodem sterk verrijkt met kalium, ammonium en fosfaat en in zuurgraad gedaald. Bovendien wordt het beschikbaar gekomen ammonium door micro-organismen vastgelegd in organische stof wat daardoor een rijk karakter krijgt. Dit effect is negen jaar na de brand nog steeds aanwezig. Het laten staan van de necromassa na de brand, zoals in Kootwijk plaatsvond, draagt niet bij aan het terugzetten van de vegetatiesuccessie naar een initieel schraal stadium, maar wel aan de diversiteit van bodemeigenschappe

The need of data harmonization to derive robust empirical relationships between soil conditions and vegetation.

Question: Is it possible to improve the general applicability and significance of empirical relationships between abiotic conditions and vegetation by harmonization of temporal data? Location: The Netherlands. Methods: Three datasets of vegetation, recorded after periods with different meteorological conditions, were used to analyze relationships between soil moisture regime (expressed by the mean spring groundwater level - MSLt calculated for different periods) and vegetation (expressed by the mean indicator value for moisture regime Fm). For each releve, measured groundwater levels were interpolated and extrapolated to daily values for the period 1970-2000 by means of an impulse-response model. Sigmoid regression lines between MSLt and Fm were determined for each of the three datasets and for the combined dataset. Results: A measurement period of three years resulted in significantly different relationships between Fm and MSLt for the three datasets (F-test,/? <0.05>. The three regression lines only coincided for the mean spring groundwater level computed over the period 1970-2000 (AfSLclimate) and thus provided a general applicable relationship. Precipitation surplus prior to vegetation recordings strongly affected the relationships. Conclusions: Harmonization of time series data (1) eliminates biased measurements, (2) results in generally applicable relationships between abiotic and vegetation characteristics and (3) increases the goodness of fit of these relationships. The presented harmonization procedure can be used to optimize many relationships between soil and vegetation characteristics. © IAVS; Opulus Press Uppsala