Image space approach to penalty methods

In this paper, we introduce a unified framework for the study of penalty concepts by means of the separation functions in the image space (see Ref. 1). Moreover, we establish new results concerning a correspondence between the solutions of the constrained problem and the limit points of the unconstrained minima. Finally, we analyze some known classes of penalty functions and some known classical results about penalization, and we show that they can be derived from our results directly.     

求解不等式约束优化问题的一个改进算法

本文改进了一个求解不等式约束优化问题的对偶算法，建立了一个相应的算法，进一步证明了该算法的收敛性．最后，给出数值结果以验证该算法的有效性。     

Optimizing Age Penalty in Time-Varying Networks with Markovian and Error-Prone Channel State

In this paper, we consider a scenario where the base station (BS) collects time-sensitive data from multiple sensors through time-varying and error-prone channels. We characterize the data freshness at the terminal end through a class of monotone increasing functions related to Age of information (AoI). Our goal is to design an optimal policy to minimize the average age penalty of all sensors in infinite horizon under bandwidth and power constraint. By formulating the scheduling problem into a constrained Markov decision process (CMDP), we reveal the threshold structure for the optimal policy and approximate the optimal decision by solving a truncated linear programming (LP). Finally, a bandwidth-truncated policy is proposed to satisfy both power and bandwidth constraint. Through theoretical analysis and numerical simulations, we prove the proposed policy is asymptotic optimal in the large sensor regime.     

Thermal-mechanical behavior of styrene-based shape memory polymer tubes

Styrene-based shape memory polymer (SMP) tubes were fabricated and their basic mechanical properties in different deformation states were investigated. The tensile, compression, bending and twisting shape memory properties of the tubes were analyzed and discussed, and the results indicated that SMP tubes exhibit good shape fixity ratio and shape recovery ratio. In addition, the shape recovery behavior was investigated at different heating rates. These experimental results will provide guidance for future applications of SMP tube structures.     

Detection of bio-constituents in complex biological tissue using Raman microscopy. Application to human nail clippings

Raman spectra of human nail clippings from various sources were collected and then deconvoluted to obtain the pure component spectra of the underlying constituents present. This blind-deconvolution was performed using a self-modeling curve resolution technique, namely band-target entropy minimization (BTEM). The aim was to simplify the complexity of the Raman spectra and hence to identify the underlying biological molecules in more detail. BTEM analysis could recover 13 pure component Raman spectral estimates from the collected 438 spectra measured from 113 nail samples. Six recovered pure component spectral estimates correspond to proteins or polypeptides that contain various amino acids such as phenylalanine, tyrosine, tryptophan, and cysteine. Two are associated with the secondary structures of proteins, and five are associated with two carotenoid species, lipid, ferulic acid, and calcium phosphate. Subsequently, the relative concentrations of these bio-constituents were calculated from the measured mixture spectra and the pure component BTEM estimates. These profiles indicated that the concentrations of some bio-constituents are correlated while others are not. A further analysis using target transformation factor analysis (TTFA) revealed the possible presence of curcumin in the human nails. Since the present approach and analysis is rather general, it might be extended to many other biological tissues in a rather straightforward and similar manner, thus revealing more detailed underlying biochemical information such as biomarkers that may be useful for diagnostic purposes.     

On the complexity of submodular function minimisation on diamonds

Let (L;?,?) be a finite lattice and let n be a positive integer. A function f:Lⁿ→R is said to be submodular if for all . In this article we study submodular functions when L is a diamond. Given oracle access to f we are interested in finding such that as efficiently as possible. We establish

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  a min–max theorem, which states that the minimum of the submodular function is equal to the maximum of a certain function defined over a certain polyhedron; and

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  a good characterisation of the minimisation problem, i.e., we show that given an oracle for computing a submodular f:Ln→Z and an integer m such that , there is a proof of this fact which can be verified in time polynomial in n and ; and

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  a pseudopolynomial-time algorithm for the minimisation problem, i.e., given an oracle for computing a submodular f:Ln→Z one can find in time bounded by a polynomial in n and .

     

Imposing no‐arbitrage conditions in implied volatilities using constrained smoothing splines

We apply constrained smoothing B‐splines to the construction of arbitrage‐free implied volatilities and derived measures. The constrained smoothing B‐splines allows the imposition of the constraints of monotonicity and convexity given by the no‐arbitrage conditions in the pricing function. We illustrate the methodology in the construction of implied volatilities and also in the construction of derived measures such as risk‐neutral densities, showing that it can be used as an effective tool for general treatment of option prices. Copyright © 2011 John Wiley & Sons, Ltd.     

Convergence analysis of a nonlinear Lagrange algorithm for general nonlinear constrained optimization problems

The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.