A Modified Integral Global Optimization Method and Its Asymptotic Convergence

In this paper, we propose a new integral global optimization algorithm for finding the solution of continuous minimization problem, and prove the asymptotic convergence of this algorithm. In our modified method we use variable measure integral, importance sampling and main idea of the cross-entropy method to ensure its convergence and efficiency. Numerical results show that the new method is very efficient in some challenging continuous global optimization problems.

NEW HMM ALGORITHM FOR TOPOLOGY OPTIMIZATION

A new hybrid MMA-MGCMMA （HMM） algorithm for solving topology optimization problems is presented. This algorithm combines the method of moving asymptotes （MMA） algorithm and the modified globally convergent version of the method of moving asymptotes （MGCMMA） algorithm in the optimization process. This algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value existing in the calculation. This algorithm can improve calculation efficiency and accelerate convergence compared with simplex MMA or MGCMMA algorithms, which is proven with an example.

Optimization Methods for Mixed Integer Weakly Concave Programming Problems

In this paper,we consider a class of mixed integer weakly concave programming problems(MIWCPP)consisting of minimizing a difference of a quadratic function and a convex function.A new necessary global optimality conditions for MIWCPP is presented in this paper.A new local optimization method for MIWCPP is designed based on the necessary global optimality conditions,which is different from the traditional local optimization method.A global optimization method is proposed by combining some auxiliary functions and the new local optimization method.Furthermore,numerical examples are also presented to show that the proposed global optimization method for MIWCPP is efficient.

Optimization Methods for Box-Constrained Nonlinear Programming Problems Based on Linear Transformation and Lagrange Interpolating Polynomials

In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optimization methods are developed.The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker(KKT)points in general.Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method.Some numerical examples are reported to show the effectiveness of the proposed methods.

A DFT study of two-dimensional P_2Si monolayer modified by single transition metal(Sc-Cu)atoms for efficient electrocatalytic CO_(2)reduction

In the present work,a stable two-dimensional(2D)P_(2)Si monolayer was predicted.The monolayer is semimetallic/metallic under the PBE/HSE06 functional and is mechanically isotropic.The stability of the P_(2)Si monolayer has been proved via cohesive energy,mechanical criteria,molecular dynamics simulation,and phonon dispersion respectively,and the monolayer possesses high carrier mobility which is three times that of Mo S_(2).On the other hand,the catalytic performance of the P_(2)Si monolayer modified with a single transition metals(M=Sc-Cu)atom for the electrochemical reduction of CO_(2)was investigated,and the monolayer can catalyze CO_(2)with three constraints:stable molecular dynamics,high migration potential of metal atoms,and suitable band gap for electrocatalyst after metal doping exhibiting excellent catalytic stabilization activity and CRR selectivity.In addition,the reduction product of V@P_(2)Si is HCOOH with an overpotential as low as 0.75 V,and the most suitable reaction path is^(*)CO_(2)→^(*)CHOO→O^(*)CHOH→^(*)+HCOOH with the final reduction product HCOOH obtained.As a whole,the above results endow the P_(2)Si monolayer to be a good 2D material holding great promises for applications in nanoelectronics and CO_(2)reduction catalysts.

Predicted a honeycomb metallic BiC and a direct semiconducting Bi_(2)C monolayer as excellent CO_(2)adsorbents

We predicted two stable two-dimensional materials of carbon and bismuth elements,namely BiC and Bi_(2)C monolayers.The stabilities of two monolayers were examined by cohesive energy,Born criteria,first-principle MD simulations and phonon spectra,respectively.By including the spin-orbit coupling effects,the BiC monolayer is a metal and the Bi_(2)C monolayer possesses a narrow direct(indirect)band gap of 0.403(0.126)eV under the HSE06(GGA-PBE)functional.For the adsorption of CO_(2)molecules,the BiC and Bi_(2)C monolayers have three stable adsorption sites C2,T3 and T4 with the adsorption energies as-0.57,-0.51 and-0.81 eV,and the activation ability on the adsorption as T4>T3>C2.These consequences make the BiC and Bi_(2)C monolayers to be promising adsorbents to capture CO_(2)gas,the Bi_(2)C monolayer to be well photovoltaics and optoelectronics material,and the BiC monolayer to be ideal battery and electronics materials,respectively.

Prediction of semiconducting SiP_(2)monolayer with negative Possion’s ratio,ultrahigh carrier mobility and CO_(2)capture ability

Using particle swarm optimization(PSO)methodology for crystal structure prediction,we predicted a novel two-dimensional(2 D)monolayer of silicide diphosphorus compound:SiP_(2),which exhibits good stability as examined via cohesive energy,mechanical criteria,molecular dynamics simulation and all positive phonon spectrum,respectively.The SiP_(2)monolayer is an indirect semiconductor with the band gap as 1.8484 eV(PBE)or 2.681 eV(HSE06),which makes it more advantageous for high-frequencyresponse optoelectronic materials.Moreover,the monolayer is a relatively hard auxetic material with negative Possion’s ratios,and also possesses a ultrahigh carrier mobility(1.069×10^(5)cm^(2)V^(-1)s^(-1))which is approximately four times the maximum value in phosphorene and comparable to the value of graphene and CP monolayers.Furthermore,the effects of strains on band structures and optical properties of SiP_(2)monolayer have been studied,as well as CO_(2)molecules can be strongly chemically adsorbed on the SiP_(2)monolayer.A semiconductor-to-metal transition for-9.5%strain ratio case and a huge optical absorption capacity on the order of 10^(6)cm^(-1)in visible region present.These theoretical findings endow SiP_(2)Monolayer to be a novel 2 D material holding great promises for applications in highperformance electronics,optoelectronics,mechanics and CO_(2)capturing material.