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This paper aims to globally solve a generalized affine fractional program problem (GAFPP). Firstly, by introducing some outer space variables and performing equivalent transformations, we can derive the equivalence problem (EP) of the GAFPP. Secondly, by constructing a novel linear relaxation method, we can deduce the affine relaxation problem (ARP) of the EP. Next, by solving the ARP to compute the lower bound, we propose a new outer space branch-and-bound algorithm for tackling the GAFPP. Then, the global convergence of the algorithm is proved, and the computational complexity of the algorithm in the worst case is analyzed. Finally, numerical experimental results are reported to illustrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

This article presents and validates a potential practical algorithm for minimizing the sum of affine fractional functions over a polyhedron. During the branch and bound search, this algorithm computes the lower bounds by solving the affine relaxation problems of the equivalent problem, which are derived by utilizing a two-level affine relaxation technique. By successive refinement and successively solving a series of affine relaxation problems, the algorithm is convergent to the global minimum of the primal problem. Moreover, the gap between the objective function and its affine relaxation function is derived for the first time, and when the partition interval tends to be infinitesimal, the gap is infinitely close to zero. Furthermore, the maximum iterations of the proposed algorithm are derived by estimating its computational complexity. Some test problems are solved to verify the potential practical and computational advantages of the algorithm. [ABSTRACT FROM AUTHOR]

This article presents and validates a new branch-and-bound algorithm for effectively solving the generalized polynomial problem (GPP). In this algorithm, a new affine relaxed technique is derived for establishing the relaxed linear programs problem of the GPP. In addition, some box reducing manipulations are employed to improve the speed of branch-and-bound search of the algorithm. Combining the relaxed linear programs problem with the box reducing manipulations, a new branch-and-bound algorithm is constructed. Some numerical examples are solved to verify the potential practical and computing advantages of the algorithm. At last, several engineering design problems are solved to validate the usefulness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an efficient outer space branch-and-bound algorithm for globally solving a minimax linear fractional programming problem (MLFP), which has a wide range of applications in data envelopment analysis, engineering optimization, management optimization, and so on. In this algorithm, by introducing auxiliary variables, we first equivalently transform the problem (MLFP) into the problem (EP). By using a new linear relaxation technique, the problem (EP) is reduced to a sequence of linear relaxation problems over the outer space rectangle, which provides the valid lower bound for the optimal value of the problem (EP). Based on the outer space branch-and-bound search and the linear relaxation problem, an outer space branch-and-bound algorithm is constructed for globally solving the problem (MLFP). In addition, the convergence and complexity of the presented algorithm are given. Finally, numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The quadratic sum-of-ratios fractional program problem has a broad range of applications in practical problems. This article will present an efficient branch-and-bound algorithm for globally solving the quadratic sum-of-ratios fractional program problem. In this algorithm, lower bounds are computed by solving a series of parametric relaxation linear programming problems, which are established by utilizing new parametric linearizing technique. To enhance the computational speed of the proposed algorithm, a rectangle reducing tactic is used to reject a part of the investigated rectangle or the whole rectangle where there does not contain any global optimal solution of the quadratic sum-of-ratios fractional program problem. Compared with the known approaches, the proposed algorithm does not need to introduce new variables and constraints. Therefore, the proposed algorithm is more suitable for application in engineering. [ABSTRACT FROM PUBLISHER]

This paper presents an outer space branch-reduction-bound algorithm for globally solving generalized affine multiplicative problems (GAMP). For finding the globally optimal solution to the GAMP, we first transform the GAMP into an equivalent problem (EP) by introducing new variables and logarithmic transformation. Next, by utilizing linearization technique of logarithmic function, the affine relaxation problem of the EP can be established for obtaining the lower bound of the optimal value to the EP. Furthermore, several outer space region reduction techniques are also presented for improving the convergence speed of this algorithm. Based on outer space search and branch-and-bound framework, a branch-reduction-bound algorithm is proposed. Finally, we prove the global convergence of the proposed algorithm, and estimate maximum iterations by analyzing its computational complexity. Some experiments are reported to show the feasibility and efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the $$l_p$$ -regularization problems, which has a broad applications in compressive sensing, variable selection problems and sparse least squares fitting for high dimensional data. We derive the exact lower bounds for the absolute value of nonzero entries in each global optimal solution of the model, which clearly demonstrates the relation between the sparsity of the optimum solution and the choice of the regularization parameter and norm. We also establish the necessary condition for global optimum solutions of $$l_p$$ -regularization problems, i.e., the global optimum solutions are fixed points of a vector thresholding operator. In addition, by selecting parameters carefully, a global minimizer which will have certain desired sparsity can be obtained. Finally, an iterative thresholding algorithm is designed for solving the $$l_p$$ -regularization problems, and any accumulation point of the sequence generated by the designed algorithm is convergent to a fixed point of the vector thresholding operator. [ABSTRACT FROM AUTHOR]

This paper presents a novel range division and contraction approach for globally solving nonconvex quadratic program with quadratic constraints. By constructing new underestimating linear relaxation functions, we can transform the initial nonconvex quadratic program problem into a linear program relaxation problem. By employing a branch and bound scheme with a range contraction approach, we describe a novel global optimization algorithm for effectively solving nonconvex quadratic program with quadratic constraints. Finally, the global convergence of the proposed algorithm is proved and numerical experimental results demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this article, we present a parametric linear relaxation algorithm for globally solving the nonconvex quadratic programming (NQP). In this algorithm, a new parametric linearized technique is proposed for generating parametric linear relaxation programming (PLRP) of the NQP, which can be used to determine the lower bound of global minimum value of the NQP. To improve the convergent speed of the proposed algorithm, a pruning operation is employed to compress the investigated region. By subdividing subsequently the initial domain and solving subsequently a series of parametric linear relaxation programming problems over the subdivided domain, the proposed algorithm is convergent to the global minimum of the NQP. Finally, an engineering problem for the design of heat exchanger network and some test examples are used to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a deterministic global optimization algorithm for solving minimax linear fractional programming (MLFP). In this algorithm, a new linearization technique is proposed, which uses more information of the objective function of the (MLFP) than other techniques. By utilizing this new linearization technique, the initial nonconvex programming problem (MLFP) is reduced to a sequence of linear relaxation programming (LRP) problems, which can provide reliable lower bound of the optimal value. The proposed algorithm is convergent to the global minimum of the (MLFP) through the successive refinement of the feasible region and solutions of a series of the (LRP). Compared with the known algorithms, numerical results show that the proposed algorithm is robust and effective. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, a global optimization algorithm is proposed for solving sum of generalized polynomial ratios problem (P) which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solve the problem (P). For such problems, we present a branch and bound algorithm. In this method, by utilizing exponent transformation and new three-level linear relaxation method, a sequence of linear relaxation programming of the initial nonconvex programming problem (P) are derived which are embedded in a branch and bound algorithm. The proposed method need not introduce new variables and constraints and it is convergent to the global minimum of prime problem by means of the subsequent solutions of a series of linear programming problems. Several numerical examples in the literatures are tested to demonstrate that the proposed algorithm can systematically solve these examples to find the approximate ϵ-global optimum. [Copyright &y& Elsevier]

Abstract: A branch and bound algorithm is proposed for globally solving a class of nonconvex programming problems (NP). For minimizing the problem, linear lower bounding functions (LLBFs) of objective function and constraint functions are constructed, then a relaxation linear programming is obtained which is solved by the simplex method and which provides the lower bound of the optimal value. The proposed algorithm is convergent to the global minimum through the successive refinement of linear relaxation of the feasible region and the solutions of a series of linear programming problems. And finally the numerical experiment is reported to show the feasibility and effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this technical note, we give a short extension application for a deterministic global optimization algorithm proposed in [Y. Ji, K.-C. Zhang, S.-J. Qu, A deterministic global optimization algorithm, Applied Mathematics and Computation 185 (2007) 382–387]. Actually our result is slightly more general, since it does not impose any special sign restrictions on numerators and denominators of the ratios. The only assumption is that the denominators of the ratios are nonzero over the feasible region of the problem. For clarity we use the same notations for the different equivalent problems and the corresponding relaxation linear programming (RLP) as done in Ji et al. (2007). [Copyright &y& Elsevier]

Abstract: In this technical note, we give a short extension application for nonlinear sum of ratios problem (P) considered in [Y.J. Wang, K.C. Zhang, Global optimization of nonlinear sum of ratios problem, Applied Mathematics and Computation 158 (2004) 319–330]. Actually our result is slightly more general, since we do not specify additional positive coefficient for each ratio. In this note, we use different equivalent problem as done in Wang and Zhang (2004). Our method introduce p variables less than other method (Wang and Zhang, 2004), and our approach need not additional special program to obtain the upper and lower bound of numerator and denominator for each ratio in the objective function. [Copyright &y& Elsevier]

Abstract: Generalized geometric programming (GGP) problem occurs frequently in engineering design and management. In this paper, a branch-and-pruning global optimization algorithm is proposed for GGP. By utilizing some transformations, a linear relaxation of the problem (GGP) is obtained based on the linear lower bound functions of objective and constraint functions inside some hyperrectangle region. Then a new pruning technique is given to accelerate the convergence of the given algorithm, and this pruning technique offers the possibility to cut away a large part of the current investigated region in which there no exist global optimum solution. The proposed algorithm which connects branch-and-bound method with the pruning technique successfully is convergent to the global minimum, according to the successive refinement of the linear relaxation of feasible region of the objective function and the solutions of a series of linear relaxation problems. And finally numerical experiment is given to illustrate the feasibility and efficiency of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper presents a branch-and-bound algorithm for globally solving a wide class of generalized linear fractional programming problems (GLFP). This class includes such problems as: minimizing a sum, or error for product of a finite number of ratios of linear functions, linear multiplicative programming, polynomial programming, etc. – over nonconvex feasible region. First a problem (Q) is derived which is equivalent to problem (GLFP). In the algorithm, lower bounds are derived by solving a sequence of linear relaxation programming problems, which is based on the construction of the linear lower bounding functions for the objective function and constraint functions of problem (Q) over the feasible region. Convergent property of the presented algorithm is proved and numerical results are given to show the feasibility of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper presents a global optimization algorithm for a class of multiplicative programming with exponent under multiplicative constraints (MPE). By utilizing equivalent problem of MPE in the sense that they have the same optimal solution, tangential hypersurfaces and concave envelope approximations a linear relaxation of equivalent problem is received. Thus the initial nonconvex programming problem (MPE) is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region of the objective function. The proposed algorithm is convergent to the globally optimal solution of MPE by means of the subsequent solutions of a series of linear programming problems. Numerical results indicate that the proposed algorithm is extremely robust and can be used successfully to solve global minimum of MPE on microcomputer. [Copyright &y& Elsevier]

We reveal that the genome of Aeromonas hydrophila HBNUAh01has an alanine racemase gene ( alr-2); this gene encodes a functional enzyme that can complement the alanine racemase deficiency of Escherichia coli strain MB2795. The gene alr-2 was cloned and expressed in E. coli BL21 (DE3). The gene has an open reading frame (ORF) of 1230 bp encoding a protein of 369 amino acids with a calculated molecular mass of 40.39 kD. The amino acid sequence deduced revealed similarity of 98, 84 and 68% with alanine racemases from A. hydrophila ATCC7966, Aeromonas caviae_Ae398, Aeromonas vickers_b565, respectively. The optimal temperature and pH for enzyme activity was 37°C and pH 10. The enzyme had broad substrate specificity. The alanine racemase was shown to belong to the pyridoxal 5′-phosphate (PLP)-dependent family of enzymes that require a certain concentration of PLP for activity. The kinetic parameters K and V at 40°C of alanine racemase were 35.9 mM, 2898 units/mg for L-alanine and 15.36 mM, 1209 units/mg for D-alanine, respectively. [ABSTRACT FROM AUTHOR]