Properties of a family of merit functions and a merit function method for the NCP

We discuss in this paper the problem of the Anomalous Microwave Emission (AME) in the light of ongoing or future observations to be performed with the largest fully steerable radio telescope in the world. High angular resolution observations of the AME will enable astronomers to drastically improve the knowledge of the AME mechanisms as well as the interplay between the different constituents of the interstellar medium in our galaxy. Extragalactic observations of the AME have started as well, and high resolution is even more important in this kind of observations. When cross-correlating with IR-dust emission, high angular resolution is also of fundamental importance in order to obtain unbiased results. The choice of the observational frequency is also of key importance in continuum observation. We calculate a merit function that accounts for the signal-to-noise ratio (SNR) in AME observation given the current state-of-the-art knowledge and technology. We also include in our merit functions the frequency dependence in the case of multifrequency observations. We briefly mention and compare the performance of four of the largest radiotelescopes in the world and hope the observational programs in each of them will be as intense as possible.

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Free-Form Reflector Design Using Differential Evolution Algorithm

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.364-366.138 ◽

2007 ◽

Vol 364-366 ◽

pp. 138-142

Author(s):

Bo Yang ◽

Guo Fan Jin ◽

Yong Tian Wang

Keyword(s):

Monte Carlo ◽

Differential Evolution ◽

Ray Tracing ◽

Differential Evolution Algorithm ◽

Merit Function ◽

Free Form ◽

Design Technique ◽

Merit Functions ◽

Nurbs Surface ◽

Evolution Algorithm

NURBS surface representation, combined with Differential Evolution (DE), enables us to perform automated non-imaging reflector design. The overall result is a simple automated nonimaging reflector design technique and only a little data such as desired illuminance distribution and searching limits are needed. Merit functions specific to non-imaging reflector design are presented. Using different merit functions, the generated illuminance distribution can be uniform as well as concentrated. DE is performed to obtain the reflector that generates the desired illuminance distribution. The photometric distributions are calculated through Monte-Carlo ray tracing and the illuminance value is used to calculate the merit function value. The validity of the proposed approach is demonstrated by optimization examples. Almost the same uniform illuminance distribution can be obtained using the algorithm proposed in this paper as that obtained by edge-raymethod. A concentrated illuminance distribution can also be generated using the algorithm proposed.

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Further Application ofH-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions

Abstract and Applied Analysis ◽

10.1155/2014/468065 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11

Author(s):

Wei-Zhe Gu ◽

Mohamed A. Tawhid

Keyword(s):

Stationary Point ◽

Complementarity Problem ◽

Global Minimum ◽

Complementarity Problems ◽

Merit Function ◽

Merit Functions ◽

Generalized Complementarity Problem ◽

Nonlinear Complementarity ◽

Generalized Complementarity Problems ◽

The Given

We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) wherefandgareH-differentiable. We describeH-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on theH-differentials offandg, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP(f,g)to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved forC1, semismooth, and locally Lipschitzian.

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The Linear Convergence of a Merit Function Method for Nonlinear Complementarity Problems

Communications in Computer and Information Science - Computational Intelligence and Intelligent Systems ◽

10.1007/978-3-642-34289-9_56 ◽

2012 ◽

pp. 503-511

Author(s):

Xiaoqin Jiang ◽

Liyong Lu

Keyword(s):

Function Method ◽

Complementarity Problems ◽

Linear Convergence ◽

Merit Function ◽

Nonlinear Complementarity Problems ◽

Nonlinear Complementarity

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Depth extraction in computational integral imaging based on bilinear interpolation

Optica Applicata ◽

10.37190/oa200401 ◽

2020 ◽

Vol 50 (4) ◽

Author(s):

Huihua Huang ◽

Peng Ge

Keyword(s):

Digital Camera ◽

Vertical Direction ◽

Merit Function ◽

Interpolation Algorithm ◽

Merit Functions ◽

Bilinear Interpolation ◽

Integral Imaging ◽

Depth Extraction ◽

Computational Integral Imaging ◽

Real Time Application

We proposed a method using a merit function to determine the depth of objects in computational integral imaging by analyzing the existing methods for depth extraction of target objects. To improve the resolution of reconstructed slice images, we use a digital camera moving in horizontal and vertical direction with the set interval to get elemental images with high resolution and bilinear interpolation algorithm to increase the number of pixels in slice image which improves the resolution obviously. To show the feasibility of the proposed method, we carried out our experiment and presented the results. We also compared it with other merit functions. The results show that merit function SMD2 to determine the depth of objects is more accurate and suitable for real-time application.

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SOME PROPERTIES OF A CLASS OF MERIT FUNCTIONS FOR SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595906000991 ◽

2006 ◽

Vol 23 (04) ◽

pp. 473-495 ◽

Cited By ~ 27

Author(s):

YONG-JIN LIU ◽

LI-WEI ZHANG ◽

YIN-HE WANG

Keyword(s):

Error Bound ◽

Complementarity Problems ◽

Symmetric Cone ◽

Merit Function ◽

Nonlinear Complementarity Problems ◽

Global Error ◽

Merit Functions ◽

Global Error Bound ◽

Nonlinear Complementarity

In this paper, we extend a class of merit functions proposed by Kanzow et al. (1997) for linear/nonlinear complementarity problems to Symmetric Cone Complementarity Problems (SCCP). We show that these functions have several interesting properties, and establish a global error bound for the solution to the SCCP as well as the level boundedness of every merit function under some mild assumptions. Moreover, several functions are demonstrated to enjoy these properties.

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An Improvement of the Concept Design Analysis Method by the Use of the Avoidance Function

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.756.382 ◽

2015 ◽

Vol 756 ◽

pp. 382-388

Author(s):

Alexander A. Khamukhin ◽

Murat H. Eres

Keyword(s):

Construction Projects ◽

Merit Function ◽

Design Analysis ◽

Concept Design ◽

Analysis Method ◽

Merit Functions ◽

Resonant Frequencies ◽

Engineering Characteristics ◽

Design Selection ◽

Bicycle Wheel

Avoiding disasters due to resonance is a major concern in construction projects such as buildings, bridges and pipelines. This paper uses the Concept Design Analysis (CODA) method that is capable of supporting the described Value-Driven Design (VDD) methodology. While VDD promotes the use of a system wide ‘value’ function during conceptual design, the CODA method allows mapping customer needs into engineering characteristics in order to calculate a single normalized design metric. The CODA method employs three different merit functions: maximizing (more is better), minimizing (less is better), and optimizing (target is better). This paper proposes a new merit function called avoidance function that allows excluding a range of engineering characteristics, e.g. avoiding a range of resonant frequencies. An example of a simple CODA model for a bicycle wheel design selection with the proposed the avoidance function is presented.

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A Two-Parametric Class of Merit Functions for the Second-Order Cone Complementarity Problem

Journal of Applied Mathematics ◽

10.1155/2013/571927 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Xiaoni Chi ◽

Zhongping Wan ◽

Zijun Hao

Keyword(s):

Complementarity Problem ◽

Unconstrained Minimization ◽

Merit Function ◽

Second Order ◽

Merit Functions ◽

New Class ◽

Second Order Cone ◽

Bounded Level Sets ◽

The One ◽

Parametric Class

We propose a two-parametric class of merit functions for the second-order cone complementarity problem (SOCCP) based on the one-parametric class of complementarity functions. By the new class of merit functions, the SOCCP can be reformulated as an unconstrained minimization problem. The new class of merit functions is shown to possess some favorable properties. In particular, it provides a global error bound ifFandGhave the joint uniform CartesianP-property. And it has bounded level sets under a weaker condition than the most available conditions. Some preliminary numerical results for solving the SOCCPs show the effectiveness of the merit function method via the new class of merit functions.

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