Objective acceleration for unconstrained optimization

Acceleration schemes can dramatically improve existing optimization procedures. In most of the work on these schemes, such as nonlinear Generalized Minimal Residual (N-GMRES), acceleration is based on minimizing the $\ell_2$ norm of some target on subspaces of $\mathbb{R}^n$. There are many numerical examples that show how accelerating general purpose and domain-specific optimizers with N-GMRES results in large improvements. We propose a natural modification to N-GMRES, which significantly improves the performance in a testing environment originally used to advocate N-GMRES. Our proposed approach, which we refer to as O-ACCEL (Objective Acceleration), is novel in that it minimizes an approximation to the \emph{objective function} on subspaces of $\mathbb{R}^n$. We prove that O-ACCEL reduces to the Full Orthogonalization Method for linear systems when the objective is quadratic, which differentiates our proposed approach from existing acceleration methods. Comparisons with L-BFGS and N-CG indicate the competitiveness of O-ACCEL. As it can be combined with domain-specific optimizers, it may also be beneficial in areas where L-BFGS or N-CG are not suitable.Comment: 18 pages, 6 figures, 5 table

Analysis of the economic adaptation of Sami reindeer management. Reindeer; source of income or cultural linkage?

The aim of this partial study is to analyse how the economies of different Sami reindeer management households are structured, and how the adaptation is structured if profit maximation is a goal. Earlier research demonstrates that different regions provides various terms. Consequently there exists a different economic structure among different households. Based on a selection of households from districts /villages from a range of geographical locations, management patterns, and region size, different economic structures are searched for. Households with similar economic structures are grouped in categories. The standard deviation confirms whether the grouping in categories. Sami Reindeer Management in Norway and Sweden has during the period from 1992/93 to 2002/03 provided recognized slaughterhouses with an even quantum of meat supply. That indicates that it probably is the same set of factors that influence the slaughter quantities of both countries. The relationship between the stock value of reindeer and the commercial value of reindeer meat, with in each household, suggests whether there is an accumulation in herd size and its magnitude. The herd increment depends on the competitive situation between the households in the district/village. As a single household cannot influence wholesale price of reindeer meat, the sales quantum is the single factor that can influence total sales. The efforts to increase herd size, due to the competitive situation, prevent the household from a maximum slaughter quantum, which thereby reduce the returns from reindeer management. Common factors for the different structures are sought for. The indication is that nether sale price of reindeer meat or line of politics influence sales quantum. The Sami reindeer herding seams to be a way of life were the size of the reindeer herd is in focus.Analys av den samiska renskötselns ekonomiska tillpassning. Renen, intäktskälla eller kulturfäste?Abstract in Swedish / Sammandrag: I denna studie analyseras hur olika renskötarhushålls ekonomier är strukturerad samt hur de tillpassar sig de ekonomiska förutsättningar som existerar för att maximera den ekonomiska avkastningen, i de fall en ekonomisk vinstmaximering är målsättningen. Tidigare forskning visar att renskötselområden uppvisar skilda betingelser. Köttförsäljningvärde, produktionsbidrag och ersättningsstorlek vid förlust av renar skiljer sig åt. Främst mellan Norge och Sverige men även regionalt inom det enskilda landet. Det medför att det existerar olika ekonomiska strukturer hos renskötarhushållen. Genom ett urval av hushåll från olika distrikt och samebyar baserat på geografisk lokalisering, driftsmönster och renskötselsområdesstorlek söks olika ekonomiska strukturer. Hushåll med liknade ekonomisk struktur grupperas i kategorier. Standardavvikelsen bekräftar om hushållen bildar en hushållskategori. Den samiska renskötseln i Norge och renskötseln Sverige har från år 1992/93 till år 2002/03 haft en kvantitetsmässigt jämn köttförsäljningsnivå till godkända slakterier. Det indikerar att det troligtvis är samma faktorer som påverkar ländernas slaktkvantitet. Förhållandet mellan lagervärde av renar och försäljningsvärdet av renkött, i det enskilda hushållet, åskådliggör om det föreligger någon tillväxt i renantalet och tillväxtens storlek. Tillväxten i renantalet beror av den konkurrenssituation som finns mellan hushållen inom distriktet/samebyn. Strävan efter att uppnå ett högre renantal, på grund av konkurrenssituationen, förhindrar hushållet att göra ett maximalt slaktuttag vilket därmed minskar avkastningen från renskötseln. Allt pekar mot att slaktkvantiteten inte påverkas av uppköpspriset på renkött eller av politiska tilltag. Den samiska renskötseln tycks vara en levnadssätt där renantalet står i centrum

Aspects of a two-pasture — herbivore model

Pastures for reindeer can be divided into green pastures (mainly herbs and grasses) of summer time and more or less snow-covered lichen pastures of winter. Fall and spring pastures have a composition in-between these extremes, but for model purposes bisection is sufficient. For the animals the green-pasture season is an anabolic phase with a physiological building-up of protein reserves, while winter is a catabolic phase where food-intake is reduced and the animals to a considerable extent survive on the accumulated reserves from summer. While protein reserves are stored from summer to winter, lichen pastures are stored from year to year. Grasses and herbs not being grazed are wilting by the end of the growing season, while lichens not grazed can live for many years. This corresponds with fundamental differences in both growth pattern and resilience. The implications of the different features, and their interconnections, are not easy to survey without formal modeling. The point of departure is a simple pasture-herbivore model, well known from the literature building on a set of differential equations. A new two-pasture-herbivore model is developed. The model includes as basic elements the Klein (1968) hypothesis and that a residual lichen biomass is kept ungrazed due to snow-cover protection. Further the annual cycle is divided into four stylized seasons with herd rates of winter survival, spring calving, summer physiological growth and fall slaughtering. Isoclines are derived for summer pasture, winter pasture and herbivores. Stability properties are discussed in relation to various situations of seasonal pasture balance. Empirical examples, particularly that of changes in pasture balance and vegetation cover in Western Finnmark, Norway, are discussed. The article finds that the two-pasture model provides important features of reality, such as the stability aspects of pasture balance, which cannot be displayed by a one-pasture model. It is suggested that this type of modeling can be used as a basis for further research, e.g. implications of climate change

Deep learning of diffeomorphisms for optimal reparametrizations of shapes

In shape analysis, one of the fundamental problems is to align curves or surfaces before computing a (geodesic) distance between these shapes. To find the optimal reparametrization realizing this alignment is a computationally demanding task which leads to an optimization problem on the diffeomorphism group. In this paper, we construct approximations of orientation-preserving diffeomorphisms by composition of elementary diffeomorphisms to solve the approximation problem. We propose a practical algorithm implemented in PyTorch which is applicable both to unparametrized curves and surfaces. We derive universal approximation results and obtain bounds for the Lipschitz constant of the obtained compositions of diffeomorphisms.Comment: 26 pages, 11 figures. Submitted to SIAM Journal of Scientific Computin

Påvirkes VO2max og Than av 14 dager med mengdetreningsregime?

Undersøke om unge idrettsutøvere påvirker Than og VO2max ved hjelp av en treningsperiode på lav intensitet over 14 dager. Resultat: Than ble forhøyet med 0.7 km/t der Than var satt til 4.0 mmol, mens VO2max ble forbedret med 1.5 ml/kg/min. Konklusjon: I dette studiet er vist at stor treningsmengde på lav intensitet har positiv påvirkning på Than og VO2max