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Aronsson, Gunnar
Publications (10 of 15) Show all publications
Aronsson, G. (2015). On Production Planning and Activity Periods. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>On Production Planning and Activity Periods
2015 (English)Report (Other academic)
Abstract [en]

Consider a company which produces and sells a certain product on a market with highly variable demand. Since the demand is very high during some periods, the company will produce and create a stock in advance before these periods. On the other hand it costs money to hold a big stock, so that some balance is needed for optimum. The demand is assumed to be known in advance with sufficient accuracy. We use a technique from optimal control theory for the analysis, which leads to so-called activity periods. During such a period the stock is positive and the production is maximal, provided that the problem starts with zero stock, which is the usual case. Over a period of one or more years, there will be a few activity periods. Outside these periods the stock is zero and the policy is to choose production = the smaller of [demand, maximal production]. The “intrinsic time length” is a central concept. It is simply the maximal time a unit of the product can be stored before selling without creating a loss.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. p. 29
Series
Linköping Studies in Economics, ISSN 1652-8166 ; 2015:2
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-113298 (URN)
Available from: 2015-01-15 Created: 2015-01-15 Last updated: 2015-09-15Bibliographically approved
Aronsson, G. (2015). Production planning, activity periods and passivity periods. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Production planning, activity periods and passivity periods
2015 (English)Report (Other academic)
Abstract [en]

Consider a company which produces and sells a certain product on a market with highly variable demand. Since the demand is very high during some periods, the company will produce and create a stock in advance before these periods. On the other hand it costs money to hold a big stock, so that some balance is needed for optimum. The demand is assumed to be known in advance with sufficient accuracy. We use a technique from optimal control theory for the analysis, which leads to so-called activity periods. During such a period the stock is positive and the production is maximal, provided that the problem starts with zero stock, which is the usual case. Over a period of one or more years, there will be a few activity periods. Outside these periods the stock is zero and the policy is to choose production = the smaller of [demand, maximal production]. The “intrinsic time length” is a central concept. It is simply the maximal time a unit of the product can be stored before selling without creating a loss.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. p. 34
Series
Linköping Studies in Economics, ISSN 1652-8166 ; 2015:3
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-123048 (URN)
Available from: 2015-12-03 Created: 2015-12-03 Last updated: 2015-12-03Bibliographically approved
Aronsson, G. & Barron, E. (2012). L-infinity Variational Problems with Running Costs and Constraints. Applied mathematics and optimization, 65(1), 53-90
Open this publication in new window or tab >>L-infinity Variational Problems with Running Costs and Constraints
2012 (English)In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 65, no 1, p. 53-90Article in journal (Refereed) Published
Abstract [en]

Various approaches are used to derive the Aronsson-Euler equations for L-infinity calculus of variations problems with constraints. The problems considered involve holonomic, nonholonomic, isoperimetric, and isosupremic constraints on the minimizer. In addition, we derive the Aronsson-Euler equation for the basic L-infinity problem with a running cost and then consider properties of an absolute minimizer. Many open problems are introduced for further study.

Place, publisher, year, edition, pages
Springer Verlag (Germany), 2012
Keywords
Calculus of variations in L-infinity; Constraints; Running cost; Aronsson-Euler equations
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-86566 (URN)10.1007/s00245-011-9151-z (DOI)000300513300004 ()
Available from: 2012-12-19 Created: 2012-12-19 Last updated: 2017-12-06
Aronsson, G. (2010). On certain minimax problems and Pontryagin’s maximum principle. Calculus of Variations and Partial Differential Equations, 37(1-2), 99-109
Open this publication in new window or tab >>On certain minimax problems and Pontryagin’s maximum principle
2010 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 37, no 1-2, p. 99-109Article in journal (Refereed) Published
Abstract [en]

This paper deals with minimax problems for nonlinear differential expressions involving a vector-valued function of a scalar variable under rather conventional structure conditions on the cost function. It is proved that an absolutely minimizing (i.e. globally and locally minimizing) function is continuously differentiable. A minimizing function is also continuously differentiable, provided a certain extra condition is satisfied. The variational method of V.G. Boltyanskii, developed within optimal control theory, is adapted and used in the proof. The case of higher order derivatives is also considered.

Place, publisher, year, edition, pages
Springer, 2010
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-67329 (URN)10.1007/s00526-009-0254-1 (DOI)
Available from: 2011-04-08 Created: 2011-04-08 Last updated: 2017-12-11
Aronsson, G. (2009). INTERPOLATION UNDER A GRADIENT BOUND. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 87(1), 19-35
Open this publication in new window or tab >>INTERPOLATION UNDER A GRADIENT BOUND
2009 (English)In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, ISSN 1446-7887, Vol. 87, no 1, p. 19-35Article in journal (Refereed) Published
Abstract [en]

This paper deals with the interpolation of given real boundary values into a bounded domain in Euclidean n-space, under a prescribed gradient bound. It is well known that there exist an upper solution (ail inf-convolution) and a lower solution (a sup-convolution) to this problem, provided that a certain compatibility condition is satisfied. If the upper and lower solutions coincide somewhere in the domain, then several interesting consequences follow. They are considered here. Basically, the upper and lower solutions must be regular wherever they coincide.

Keywords
eikonal, infimal convolution, supremal convolution, interpolation, uniqueness set, weighted length, shortest curve, optimal control, maximum principle, semiconcave
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-51279 (URN)10.1017/S1446788709000044 (DOI)
Available from: 2009-10-26 Created: 2009-10-26 Last updated: 2009-10-26
Aronsson, G. (2008). On certain minimax problems and the Pontryagin maximum principle. Linköping: Linköpings universitet
Open this publication in new window or tab >>On certain minimax problems and the Pontryagin maximum principle
2008 (English)Report (Other academic)
Abstract [en]

  

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2008
Series
LiTH-MAI-R ; 6
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-42611 (URN)66899 (Local ID)66899 (Archive number)66899 (OAI)
Available from: 2009-10-10 Created: 2009-10-10
Aronsson, G. (2007). Interpolation under a gradient bound and infimal convolutions. Linköping: Linköpings universitet
Open this publication in new window or tab >>Interpolation under a gradient bound and infimal convolutions
2007 (English)Report (Other academic)
Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2007
Series
LiTH-MAT-R ; 2
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-37877 (URN)LiTH-MAT-R-2007-02-SE (ISRN)40145 (Local ID)40145 (Archive number)40145 (OAI)
Available from: 2009-10-10 Created: 2009-10-10
Aronsson, G. (2006). Examples of infinity harmonic functions having singular lines. Linköping: Linköpings universitet
Open this publication in new window or tab >>Examples of infinity harmonic functions having singular lines
2006 (English)Report (Other academic)
Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2006. p. 20
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2006:3
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-32842 (URN)2006-03 (ISRN)18780 (Local ID)18780 (Archive number)18780 (OAI)
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2011-03-09Bibliographically approved
Aronsson, G., Crandall, M. G. & Juutinen, P. (2004). A Tour of the Theory of Absolutely Minimizing Functions. Linköping: Linköpings universitet
Open this publication in new window or tab >>A Tour of the Theory of Absolutely Minimizing Functions
2004 (English)Report (Other academic)
Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2004
Series
LiTH-MAT-R ; 2
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-23716 (URN)3219 (Local ID)3219 (Archive number)3219 (OAI)
Available from: 2009-10-07 Created: 2009-10-07
Aronsson, G., Crandall, M. & Juutinen, P. (2004). A tour of the theory of absolutely minimizing functions. Bulletin of the American Mathematical Society, 41(4), 439-505
Open this publication in new window or tab >>A tour of the theory of absolutely minimizing functions
2004 (English)In: Bulletin of the American Mathematical Society, ISSN 0273-0979, E-ISSN 1088-9485, Vol. 41, no 4, p. 439-505Article in journal (Refereed) Published
Abstract [en]

These notes are intended to be a rather complete and self-contained exposition of the theory of absolutely minimizing Lipschitz extensions, presented in detail and in a form accessible to readers without any prior knowledge of the subject. In particular, we improve known results regarding existence via arguments that are simpler than those that can be found in the literature. We present a proof of the main known uniqueness result which is largely self-contained and does not rely on the theory of viscosity solutions. A unifying idea in our approach is the use of cone functions. This elementary geometric device renders the theory versatile and transparent. A number of tools and issues routinely encountered in the theory of elliptic partial differential equations are illustrated here in an especially clean manner, free from burdensome technicalities - indeed, usually free from partial differential equations themselves. These include a priori continuity estimates, the Harnack inequality, Perron's method for proving existence results, uniqueness and regularity questions, and some basic tools of viscosity solution theory. We believe that our presentation provides a unified summary of the existing theory as well as new results of interest to experts and researchers and, at the same time, a source which can be used for introducing students to some significant analytical tools.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-45621 (URN)10.1090/S0273-0979-04-01035-3 (DOI)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13
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