The convergence of subspace trust region methods

AbstractThe trust region method is an effective approach for solving optimization problems due to its robustness and strong convergence. However, the subproblem in the trust region method is difficult or time-consuming to solve in practical computation, especially in large-scale problems. In this paper we consider a new class of trust region methods, specifically subspace trust region methods. The subproblem in these methods has an adequate initial trust region radius and can be solved in a simple subspace. It is easier to solve than the original subproblem because the dimension of the subproblem in the subspace is reduced substantially. We investigate the global convergence and convergence rate of these methods

Terahertz Atmospheric Windows for High Angular Resolution Terahertz Astronomy from Dome A

Atmospheric transmission from Dome A, Antarctica, presents new possibilities in the field of terahertz astronomy, where space telescopes have been the only observational tools until now. Using atmospheric transmission measurements from Dome A with a Fourier transform spectrometer, transmission spectra and long-term stabilities have been analyzed at 1.461 THz, 3.393 THz, 5.786 THz and 7.1 THz, which show that important atmospheric windows for terahertz astronomy open for a reasonable length of time in the winter season. With large aperture terahertz telescopes and interferometers at Dome A, high angular resolution terahertz observations are foreseen of atomic fine-structure lines from ionized gas and a water ice feature from protoplanetary disks.Comment: 6 pages, 3 figures, to appear in Advances in Polar Scienc

New Inexact Line Search Method for Unconstrained Optimization

We propose a new inexact line search rule and analyze the global convergence and convergence rate of related descent methods. The new line search rule is similar to the Armijo line-search rule and contains it as a special case. We can choose a larger stepsize in each line-search procedure and maintain the global convergence of related line-search methods. This idea can make us design new line-search methods in some wider sense. In some special cases, the new descent method can reduce to the Barzilai and Borewein method. Numerical results show that the new line-search methods are efficient for solving unconstrained optimization problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45195/1/10957_2005_Article_6553.pd

On memory gradient method with trust region for unconstrained optimization

In this paper we present a new memory gradient method with trust region for unconstrained optimization problems. The method combines line search method and trust region method to generate new iterative points at each iteration and therefore has both advantages of line search method and trust region method. It sufficiently uses the previous multi-step iterative information at each iteration and avoids the storage and computation of matrices associated with the Hessian of objective functions, so that it is suitable to solve large scale optimization problems. We also design an implementable version of this method and analyze its global convergence under weak conditions. This idea enables us to design some quick convergent, effective, and robust algorithms since it uses more information from previous iterative steps. Numerical experiments show that the new method is effective, stable and robust in practical computation, compared with other similar methods.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45437/1/11075_2005_Article_9008.pd

Bis(4-acetyl-3-methyl-1-phenyl-1H-pyrazol-5-olato-κ2 O,O′)bis­(N,N-dimethyl­formamide-κO)nickel(II)

The title complex, [Ni(C12H11N2O2)2(C3H7NO)2], lies on on an inversion center. The NiII ion is coordinated in a slightly distorted octa­hedral coordination enviroment by four O atoms from two bis-chelating 4-acety-3-methyl-1-phenyl-1H-pyrazol-5-olate ligands in the equatorial plane and two O atoms from two N,N-dimethyl­formamide ligands in the axial sites. In the crystal structure, weak inter­molecular π–π stacking inter­actions with centroid–centroid distances of 3.7467 (13) Å link mol­ecules into chains extending alongthe b axis

Simple bots breed social punishment in humans

Costly punishment has been suggested as a key mechanism for stabilizing cooperation in one-shot games. However, recent studies have revealed that the effectiveness of costly punishment can be diminished by second-order free riders (i.e., cooperators who never punish defectors) and antisocial punishers (i.e., defectors who punish cooperators). In a two-stage prisoner's dilemma game, players not only need to choose between cooperation and defection in the first stage, but also need to decide whether to punish their opponent in the second stage. Here, we extend the theory of punishment in one-shot games by introducing simple bots, who consistently choose prosocial punishment and do not change their actions over time. We find that this simple extension of the game allows prosocial punishment to dominate in well-mixed and networked populations, and that the minimum fraction of bots required for the dominance of prosocial punishment monotonically increases with increasing dilemma strength. Furthermore, if humans possess a learning bias toward a "copy the majority" rule or if bots are present at higher degree nodes in scale-free networks, the fully dominance of prosocial punishment is still possible at a high dilemma strength. These results indicate that introducing bots can be a significant factor in establishing prosocial punishment. We therefore, provide a novel explanation for the evolution of prosocial punishment, and note that the contrasting results that emerge from the introduction of different types of bots also imply that the design of the bots matters.Comment: 12 pages, 4 figure

Improved particle swarm optimization algorithm for multi-reservoir system operation

AbstractIn this paper, a hybrid improved particle swarm optimization (IPSO) algorithm is proposed for the optimization of hydroelectric power scheduling in multi-reservoir systems. The conventional particle swarm optimization (PSO) algorithm is improved in two ways: (1) The linearly decreasing inertia weight coefficient (LDIWC) is replaced by a self-adaptive exponential inertia weight coefficient (SEIWC), which could make the PSO algorithm more balanceable and more effective in both global and local searches. (2) The crossover and mutation idea inspired by the genetic algorithm (GA) is imported into the particle updating method to enhance the diversity of populations. The potential ability of IPSO in nonlinear numerical function optimization was first tested with three classical benchmark functions. Then, a long-term multi-reservoir system operation model based on IPSO was designed and a case study was carried out in the Minjiang Basin in China, where there is a power system consisting of 26 hydroelectric power plants. The scheduling results of the IPSO algorithm were found to outperform PSO and to be comparable with the results of the dynamic programming successive approximation (DPSA) algorithm