We describe an algorithm for linear and convex quadratic programming problems that uses power series approximation of the weighted barrier path that passes through the current iterate in order to find the next iterate. If r > 1 is the order of approximation used, we show that our algorithm has time complexity O(n t(+l/r)L(l+l/r)) iterations and O(n3 + n2r) arithmetic operations per iteration, where n is the dimension of the problem and L is the size of the input data. When r = 1, we show that the algorithm can be interpreted as an affine scaling algorithm in the primal-dual setup. Introduction. After the presentation of the new polynomial-time algorithm for linear programming byKarmarkar in his landmark paper [15], several so-called interior point algorithms for linear and convex quadratic programming have been proposed. These algorithms can be classified into three main groups: (a) Projective algorithms, e.g. [3], [4], [8], [14], [15], [29] and [34]. (b) Affine scaling algorithms, originally proposed by Dikin [9]. See also [1], [5], [10] and [33]. (c) Path following algorithms, e.g. [13], [18], [19], [24], [25], [26], [28] and [32].The algorithms of class (a) are known to have polynomial-time complexity requiring O(nL) iterations. However, these methods appear not to perform well in practice [30]. In contrast, the algorithms of group (b), while not known to have polynomial-time complexity, have exhibited good behavior on real world linear programs [1], [20], [23], [31]. Most path following algorithms of group (c) have been shown to require O(/n L) iterations. These algorithms use Newton's method to trace the path of minimizers for the logarithmic barrier family of problems, the so-called central path. The logarithmic barrier function approach is usually attributed to Frisch [12] and is formally studied in Fiacco and McCormick [11] in the context of nonlinear optimization. Continuous trajectories for interior point methods were proposed by Karmarkar [16] and are extensively studied in Bayer and Lagarias [6] [7], Megiddo [21] and Megiddo and Shub [22]. Megiddo [21] related the central path to the classical barrier path in the framework of the primal-dual complementarity relationship. Kojima, Mizuno and Yoshise [19] used this framework to describe a primal-dual interior point algorithm that traces the central trajectory and has a worst time complexity of O(nL) iterations. Monteiro and Adler [25] present a path following primal-dual algorithm that requires O(Vn L) iterations.This paper describes a modification of the algorithm of Monteiro and Adler [25] and shows that the resulting algorithm can be interpreted as an affine scaling algorithm in the primal-dual setting. We also show polynomial-time convergence for the primal-dual affine scaling algorithm by using a readily available starting primal-dual solution lying on the central path and a suitable fixed step size. Furthermore, we show finite global convergence (not necessarily polynomial) for any starting primal-dual solution. In [21] it is shown that there exist...

RESUMO:Com o objetivo de avaliar o impacto ambiental ocorrido na área experimental do Departamento de Entomologia -ESALQ/USP, num período de 25 anos, aplicou-se a análise faunística aos resultados da coleta de insetos, com armadilha luminosa, em 1965/66 e 1990/91. Comparando-se os índices fisiográficos das épocas estudadas, verifica-se uma redução de 35,1% entre 1965/66 e 1990/91. Como conseqüência, o índice de diversidade também diminuiu em 60,3% nas datas estudadas, em decorrência da menor coleta de insetos, caracterizando considerável impacto ambiental. Descritores: índices faunísticos, armadilha luminosa, ambiente FAUNISTIC INSECT ANALYSIS FOR ENVIRONMENTAL CHANGE EVALUATIONABSTRACT: Environmental changes at the experimental area of the Department of Entomology, University of São Paulo, in Piracicaba, in a period of 25 years, were evaluated using a faunistc insect analysis of samples collected by light traps in 1965/66 and 1990/91. A reduction of 35.1% in the faunistic index between these two periods was recorded. Consequently, the diversity index also decreased by 60.3% due to the low number of insects collected. These indices suggest a considerable environmental change in the experimental area over this 25 years period.

RESUMOEste estudo apresenta a estrutura de florestas em Gaúcha do Norte-MT (13° 10'S e 53° 15' O), na borda sul-amazônica. Para o levantamento fitossociológico, três áreas amostrais de 1ha foram subdivididas em 50 parcelas de 10x20m, nas quais foram amostrados todos os indivíduos com perímetro à altura do peito (PAP) $15 cm. Para verificar a similaridade estrutural entre as áreas utilizou-se a Análise de Correspondência. As espécies indicadoras dos ambientes de interflúvio e das áreas sujeitas à inundação foram obtidas através do TWINSPAN e de um sistema de pesos. Concluiu-se que as florestas presentes na bacia do rio Pacuneiro pertencem à mesma unidade fitogeográfica, mas com subtipos florísticos e estruturais de acordo com a posição no relevo, a proximidade dos cursos d'água e o estrato analisado, apresentando predominância de algumas espécies, ou até mesmo possíveis endemismos, em determinados trechos ou estratos. A formação apresentou baixa diversidade alfa (2,91 a 3,50) e beta (3,62 a 3,86), o que não é comum em florestas amazônicas. Várias hipóteses podem explicar essa baixa diversidade, entre elas a baixa precipitação e a alta sazonalidade, o ambiente físico regional aparentemente homogêneo e favorável às espécies competidoras, ou os eventos históricos, relacionados à possível exploração por tribos indígenas ou à recente expansão dessas florestas sobre as áreas savânicas. PALAVRAS-CHAVEAmazônia, Xingu, floresta Amazônica, estrutura florestal. Structure of patch of Amazonian forest in the alto

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