66 research outputs found
Central Paths and Selection of Equilibria
For two populations of players playing repeatedly a same bimatrix game, a dynamics associated with the method of analytic centers for linear programming is described. All populations' evolutions converge to static equilibria. All evolutions starting in a same connected set converge to a same equilibrium. If a starting time is sufficiently large, "almost all" evolutions end up at a single equilibrium representing all populations' pure strategy groups (phenotypes) with nonzero proportions. The dynamics is interpreted as populations' rule to learn best replying
Central Path Curvature and Iteration-Complexity for Redundant Klee—Minty Cubes
We consider a family of linear optimization problems over the n-dimensional Klee—Minty cube and show that the central path may visit all of its vertices in the same order as simplex methods do. This is achieved by carefully adding an exponential number of redundant constraints that forces the central path to take at least 2n − 2 sharp turns. This fact sug-gests that any feasible path-following interior-point method will take at least O(2n) iterations to solve this problem, whereas in practice typically only a few iterations (e.g., 50) suffices to obtain a high-quality solution. Thus, the construction potentially exhibits the worst-case iteration-complexity known to date which almost matches the theoretical iteration-complexity bound for this type of methods. In addition, this construction gives a counterexample to a conjecture that the total central path curvature is O(n)
A Class of Large-Update and Small-Update Primal-Dual Interior-Point Algorithms for Linear Optimization
Comments on: Recent progress on the combinatorial diameter of polytopes and simplicial complexes
The characterization and antibiotic resistance profiles of clinical Escherichia coli O25b-B2-ST131 isolates in Kuwait
High prevalence of oxacillinases in clinical multidrug-resistant Acinetobacter baumannii isolates from the Tshwane region, South Africa – an update
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