There is no variational characterization of the cycles in the method of periodic projections

The method of periodic projections consists in iterating projections onto $m$ closed convex subsets of a Hilbert space according to a periodic sweeping strategy. In the presence of $m\geq 3$ sets, a long-standing question going back to the 1960s is whether the limit cycles obtained by such a process can be characterized as the minimizers of a certain functional. In this paper we answer this question in the negative. Projection algorithms that minimize smooth convex functions over a product of convex sets are also discussed

Price of Anarchy in Bernoulli Congestion Games with Affine Costs

We consider an atomic congestion game in which each player participates in the game with an exogenous and known probability $p_{i}\in[0,1]$, independently of everybody else, or stays out and incurs no cost. We first prove that the resulting game is potential. Then, we compute the parameterized price of anarchy to characterize the impact of demand uncertainty on the efficiency of selfish behavior. It turns out that the price of anarchy as a function of the maximum participation probability $p=\max_{i} p_{i}$ is a nondecreasing function. The worst case is attained when players have the same participation probabilities $p_{i}\equiv p$. For the case of affine costs, we provide an analytic expression for the parameterized price of anarchy as a function of $p$. This function is continuous on $(0,1]$, is equal to $4/3$ for $0<p\leq 1/4$, and increases towards $5/2$ when $p\to 1$. Our work can be interpreted as providing a continuous transition between the price of anarchy of nonatomic and atomic games, which are the extremes of the price of anarchy function we characterize. We show that these bounds are tight and are attained on routing games -- as opposed to general congestion games -- with purely linear costs (i.e., with no constant terms).Comment: 29 pages, 6 figure

A Dynamical Approach to Convex Minimization Coupling Approximation with the Steepest Descent Method

AbstractWe study the asymptotic behavior of the solutions to evolution equations of the form 0∈u(t)+∂f(u(t), ε(t));  u(0)=u0, where {f(·, ε):ε>0} is a family of strictly convex functions whose minimum is attained at a unique pointx(ε). Assuming thatx(ε) converges to a pointx* as ε tends to 0, and depending on the behavior of the optimal trajectoryx(ε), we derive sufficient conditions on the parametrization ε(t) which ensure that the solutionu(t) of the evolution equation also converges tox* whent→+∞. The results are illustrated on three different penalty and viscosity-approximation methods for convex minimization

In-between Wor(l)ds: female autofiction and postcolonial identity in Marie Cardinal´s Au pays de mes racines, Marguerite Duras´s L´amant and Isabela Figueiredo´s Caderno de Memórias Coloniais

Female autofiction can be considered as a form of feminist confessional since, by challenging dominant configurations of knowledge – such as those embodied by autobiographism – and drawing attention to women’s personal issues, it aims at articulating the multiplicity of the female narrative subject. Autofictional works such as Marie Cardinal’s Au pays de mes racines [In the Country of my Roots], Marguerite Duras’s L’amant [The Lover] and Isabela Figueiredo’s Caderno de Memórias Coloniais [Notebook of Colonial Memories] can therefore be viewed as dealing with female personal concerns in a political way. This is because their exploration of women’s marginal status in formerly colonial countries like Algeria, Indochina and Mozambique, functions as an empowering tool through which they challenge the structures of domination impinging on their identity while asserting their own individuality. The purpose of this dissertation is to explore how the literary genre of autofiction harmonizes with and serves to better articulate issues of female subjectivity and cultural hybridization, particularly as concerns the power dynamics at stake in the narratives’ transcultural contexts. The focus will be on the fragmented sense of self imbuing these novels and which is directly related to the liminal status occupied by the narrators who are in-between different cultures. The final objective is to investigate how the notion of in-betweenness, which underlies both the genre of autofiction itself and the structure of the texts, can function as a feminist category of representation of women’s subjectivity and which defies oppressive social conventions related to patriarchal colonial patterns