Fundamentals of Convex Analysis

“…For this, we use basic tools from convex analysis and geometry. Readers not familiar with this field may use [17] (especially its Chap. C) for an elementary introduction, while [16,22] are more complete.…”

Section: Introducing Cut-generating Functionsmentioning

confidence: 99%

Cut-Generating Functions and S-Free Sets

et al. 2015

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We consider the separation problem for sets X that are pre-images of a given set S by a linear mapping. Classical examples occur in integer programming, as well as in other optimization problems such as complementarity. One would like to generate valid inequalities that cut off some point not lying in X, without reference to the linear mapping. To this aim, we introduce a concept: cut-generating functions (cgf) and we develop a formal theory for them, largely based on convex analysis. They are intimately related to S-free sets and we study this relation, disclosing several definitions for minimal cgf's and maximal S-free sets. Our work unifies and puts in perspective a number of existing works on S-free sets; in particular, we show how cgf's recover the celebrated Gomory cuts.

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“…The proof of a more general result can be found in [14] (Chapter E, Proposition 1.3.9(ii)). Denote by q t the strategy, constructed in Theorem 3, where F is replaced by F. We claim that F( q t ) = F( q t ), a.e.…”

Section: Cooperative Harvesting Problem: the Case Of Non-concave Revementioning

confidence: 99%

Rational taxation in an open access fishery model

Rokhlin¹,

Усов²

2017

Archives of Control Sciences

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We consider a model of fishery management, where n agents exploit a single population with strictly concave continuously differentiable growth function of Verhulst type. If the agent actions are coordinated and directed towards the maximization of the discounted cooperative revenue, then the biomass stabilizes at the level, defined by the well known "golden rule". We show that for independent myopic harvesting agents such optimal (or ε-optimal) cooperative behavior can be stimulated by the proportional tax, depending on the resource stock, and equal to the marginal value function of the cooperative problem. To implement this taxation scheme we prove that the mentioned value function is strictly concave and continuously differentiable, although the instantaneous individual revenues may be neither concave nor differentiable.

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Fundamentals of Convex Analysis

Cited by 975 publications

References 0 publications

On the Chvátal-Gomory Closure of a Compact Convex Set

On the Chvátal-Gomory Closure of a Compact Convex Set

Cut-Generating Functions and S-Free Sets

Rational taxation in an open access fishery model

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