Disciplined geometric programming

Agrawal, Akshay; Diamond, Steven; Boyd, Stephen

doi:10.1007/s11590-019-01422-z

Cited by 31 publications

(27 citation statements)

References 39 publications

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“…We also note that problem 12 is log-log convex [26] with the obvious change of variables. While we do not explore this connection here, we suspect that this approach might provide a simple way of stating what class of functions can be used as an automated market maker mechanism such that the resulting no-arbitrage bounds are useful.…”

Section: F the Arbitrage Problem In Constant Mean Marketsmentioning

confidence: 99%

An Analysis of Uniswap markets

Angeris

Kao²,

Chiang³

et al. 2020

Cryptoeconomic Systems

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Uniswap-and other constant product markets-appear to work well in practice despite their simplicity. In this paper, we give a simple formal analysis of constant product markets and their generalizations, showing that, under some common conditions, these markets must closely track the reference market price. We also show that Uniswap satisfies many other desirable properties and numerically demonstrate, via a large-scale agent-based simulation, that Uniswap is stable under a wide range of market conditions.

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Section: F the Arbitrage Problem In Constant Mean Marketsmentioning

confidence: 99%

An Analysis of Uniswap markets

Angeris

Kao²,

Chiang³

et al. 2020

Cryptoeconomic Systems

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“…The interpretation of the experimental evidence might require Zener's geometric programming optimizations [117]: geometric programming is a nonlinear mathematical optimization method used to minimize functions that are in the form of polynomials subject to constraints of the same type. The connection between geometric programming and the Darwin-Fowler method has been established since some time [117] (see also a modern approach [118]). Since the data used in the optimization procedure are always affected by errors and uncertainties, a strategy to handle them is provided by the theory of Fuzzy sets, as discussed very recently [119], for example in reference [4], in generally in most of our work we used the generalized simulated annealing (GSA) [120].…”

Section: Discussionmentioning

confidence: 99%

From the Kinetic Theory of Gases to the Kinetics of Rate Processes: On the Verge of the Thermodynamic and Kinetic Limits

2020

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A variety of current experiments and molecular dynamics computations are expanding our understanding of rate processes occurring in extreme environments, especially at low temperatures, where deviations from linearity of Arrhenius plots are revealed. The thermodynamic behavior of molecular systems is determined at a specific temperature within conditions on large volume and number of particles at a given density (the thermodynamic limit): on the other side, kinetic features are intuitively perceived as defined in a range between the extreme temperatures, which limit the existence of each specific phase. In this paper, extending the statistical mechanics approach due to Fowler and collaborators, ensembles and partition functions are defined to evaluate initial state averages and activation energies involved in the kinetics of rate processes. A key step is delayed access to the thermodynamic limit when conditions on a large volume and number of particles are not fulfilled: the involved mathematical analysis requires consideration of the role of the succession for the exponential function due to Euler, precursor to the Poisson and Boltzmann classical distributions, recently discussed. Arguments are presented to demonstrate that a universal feature emerges: Convex Arrhenius plots (super-Arrhenius behavior) as temperature decreases are amply documented in progressively wider contexts, such as viscosity and glass transitions, biological processes, enzymatic catalysis, plasma catalysis, geochemical fluidity, and chemical reactions involving collective phenomena. The treatment expands the classical Tolman’s theorem formulated quantally by Fowler and Guggenheim: the activation energy of processes is related to the averages of microscopic energies. We previously introduced the concept of “transitivity”, a function that compactly accounts for the development of heuristic formulas and suggests the search for universal behavior. The velocity distribution function far from the thermodynamic limit is illustrated; the fraction of molecules with energy in excess of a certain threshold for the description of the kinetics of low-temperature transitions and of non-equilibrium reaction rates is derived. Uniform extension beyond the classical case to include quantum tunneling (leading to the concavity of plots, sub-Arrhenius behavior) and to Fermi and Bose statistics has been considered elsewhere. A companion paper presents a computational code permitting applications to a variety of phenomena and provides further examples.

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“…These posynomial constraints are not directly convex; rather, ln (p(e z )) is convex in z, and x = e z can be calculated after solving. Geometric Programs also be expressed in terms of exponential cone constraints [2].…”

Section: Geometric Programsmentioning

confidence: 99%

“…It did so by embracing a participatory human-centered framework focused on validating workers' knowledge [26] and using connections between that knowledge and the mathematics of optimization to develop GPkit, a toolkit for convex Geometric Programs. GPkit was used by many engineers and researchers during its development [1,2,11,14,16,17,27,28,32,33,36,46,48,49,53,60,64,68], which resulted in features that are:…”

Section: Introductionmentioning

confidence: 99%

GPkit: A Human-Centered Approach to Convex Optimization in Engineering Design

Burnell

Damen

Hoburg

2020

Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems

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We present GPkit, a Python toolkit for Geometric and Signomial Programming that prioritizes explainability and incremental complexity. GPkit was designed through an ethnographic approach in the firms, classrooms, and research labs where it became part of the fabric of daily engineering work. Organizations have approached GPkit both in ways which centralize design work and in ways which distribute it, usecases which emerged from and inspired new toolkit features. This twoway flow between mathematical structure and practitioner knowledge resulted in several novel contributions to the formulation and interpretation of convex programs and to our understanding of early-stage engineering design. For example, dual solutions (often considered incidental) can be more valuable to a design process than the "optimal design" itself, and we present novel algorithms and design methods based on this insight.

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Disciplined geometric programming

Cited by 31 publications

References 39 publications

An Analysis of Uniswap markets

An Analysis of Uniswap markets

From the Kinetic Theory of Gases to the Kinetics of Rate Processes: On the Verge of the Thermodynamic and Kinetic Limits

GPkit: A Human-Centered Approach to Convex Optimization in Engineering Design

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