Hessian barrier algorithms for linearly constrained optimization problems

In this paper, we propose an interior-point method for linearly constrained optimization problems (possibly nonconvex). The method - which we call the Hessian barrier algorithm (HBA) - combines a forward Euler discretization of Hessian Riemannian gradient flows with an Armijo backtracking step-size policy. In this way, HBA can be seen as an alternative to mirror descent (MD), and contains as special cases the affine scaling algorithm, regularized Newton processes, and several other iterative solution methods. Our main result is that, modulo a non-degeneracy condition, the algorithm converges to the problem's set of critical points; hence, in the convex case, the algorithm converges globally to the problem's minimum set. In the case of linearly constrained quadratic programs (not necessarily convex), we also show that the method's convergence rate is $\mathcal{O}(1/k^\rho)$ for some $\rho\in(0,1]$ that depends only on the choice of kernel function (i.e., not on the problem's primitives). These theoretical results are validated by numerical experiments in standard non-convex test functions and large-scale traffic assignment problems.Comment: 27 pages, 6 figure

Constrained Interactions and Social Coordination

We consider a co-evolutionary model of social coordination and network formation where agents may decide on an action in a 2x2 - coordination game and on whom to establish costly links to. We find that a payoff domination convention is selected for a wider parameter range when agents may only support a limited number of links as compared to a scenario where agents are not constrained in their linking choice. The main reason behind this result is that whenever there is a small cluster of agents playing the efficient strategy other players want to link up to those layers and choose the efficient action

A competitive search game with a moving target

We introduce a discrete-time search game, in which two players compete to find an invisible object first. The object moves according to a time-varying Markov chain on finitely many states. The players are active in turns. At each period, the active player chooses a state. If the object is there then he finds the object and wins. Otherwise the object moves and the game enters the next period. We show that this game admits a value, and for any error-term epsilon > 0 , each player has a pure (subgame-perfect) epsilon-optimal strategy. Interestingly, a 0-optimal strategy does not always exist. We derive results on the analytic and structural properties of the value and the epsilon-optimal strategies. We devote special attention to the important timehomogeneous case, where we show that (subgame-perfect) optimal strategies exist if the Markov chain is irreducible and aperiodic

Hessian barrier algorithms for linearly constrained optimization problems

International audienceIn this paper, we propose an interior-point method for linearly constrained-and possibly nonconvex-optimization problems. The method-which we call the Hessian barrier algorithm (HBA)-combines a forward Euler discretization of Hessian-Riemannian gradient flows with an Armijo backtracking step-size policy. In this way, HBA can be seen as an alternative to mirror descent, and contains as special cases the affine scaling algorithm, regularized Newton processes, and several other iterative solution methods. Our main result is that, modulo a nondegeneracy condition, the algorithm converges to the problem's critical set; hence, in the convex case, the algorithm converges globally to the problem's minimum set. In the case of linearly constrained quadratic programs (not necessarily convex), we also show that the method's convergence rate is $O(1/k^\rho)$ for some $\rho \in (0, 1]$ that depends only on the choice of kernel function (i.e., not on the problem's primi-tives). These theoretical results are validated by numerical experiments in standard nonconvex test functions and large-scale traffic assignment problems

Beiträge zur Geschichte des Landkreises Regensburg 40

Marginalien von 12 Autoren, darin: Sparkasse Regensburg: Silbermedaille 'Mittelalter in Ostbayern' (S. 3); Fendl, Josef: Heimatgeschichte in zwei Dialekt-Monologen (S. 3-6); Deml, Hans: Eine Karriere im Mittelalter: Hans Vetter aus "Kohlßriedt" (S. 7); Schwaiger, Dieter: Kriegsnöte in der Pfarrei Deuerling (S. 8-11); Donau Post: Frauenzells großer Baumeister kam aus Wörth (S. 12); Raab, Michael: Großer Hexenprozeß zu Geisling 1689-1691 (S. 13-17); Lermer, Xaver: Die Donau (bei Geisling) / Haidau - Haidauer Weg / Das Jahr 1809 (S. 18-21); Mittelbayerische Zeitung: Zwei Aufsätze zur Schulgeschichte Altenthanns: Für Bemühungen wird nur Spott und Grobheit gebracht - Von Altenthann wollten junge Lehrer sofort wieder weg, Bei unehelichen Kindern verlor Altenthann die Geduld (S. 22-25); Donau Post: In Wolfskofen fanden sie eine neue Heimat (S. 25-26); Mittelbayerische Zeitung: Vor 25 Jahren Fähre von Pfatter nach Wörth eingestellt - Beim Uferer Karl Schiller gingen die Nazi-Größen baden (S. 27); Staudigl, Franz Xaver: Kampf um die Glaubens- und Gewissensfreiheit (S. 28-36); Koschier, Franz: Der Festzug - Hinweise für Organisation und Gestaltung (S. 37-40); Fendl, Josef: Die Kapelle bei St. Johann (S. 40

Local interactions under switching costs

We study the impact of switching costs on the long-run outcome in 2×2 coordination games played in the circular city model of local interactions. For low levels of switching costs, the predictions are in line with the previous literature and the risk-dominant convention is the unique long-run equilibrium. For intermediate levels of switching costs, the set of long-run equilibria still contain the risk-dominant convention but may also contain conventions that are not risk dominant. The set of long-run equilibria may further be non-monotonic in the level of switching costs, i.e., as switching costs increase the prediction that the risk-dominant convention is the unique long-run equilibrium and the prediction that both conventions are long-run equilibria alternate. Finally, for high levels of switching costs, also non-monomorphic states will be included in the set of long-run equilibria

The Temporal Signature of Memories: Identification of a General Mechanism for Dynamic Memory Replay in Humans

Reinstatement of dynamic memories requires the replay of neural patterns that unfold over time in a similar manner as during perception. However, little is known about the mechanisms that guide such a temporally structured replay in humans, because previous studies used either unsuitable methods or paradigms to address this question. Here, we overcome these limitations by developing a new analysis method to detect the replay of temporal patterns in a paradigm that requires participants to mentally replay short sound or video clips. We show that memory reinstatement is accompanied by a decrease of low-frequency (8 Hz) power, which carries a temporal phase signature of the replayed stimulus. These replay effects were evident in the visual as well as in the auditory domain and were localized to sensory-specific regions. These results suggest low-frequency phase to be a domain-general mechanism that orchestrates dynamic memory replay in humans