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• All the transformation parameters including those of translation are regularized in our CVPR paper, causing the method not able to handle un- known arbitrary translations. To address this issue, we show that under a mild condition, the objective function of RPM is strictly convex quadratic w.r.t. translation. Thus, translation can first be eliminated via minimization. Then, we only need to enforce regularization on the non-translational part of the transformation. This enables our algorithm to handle unknown arbitrary translations and more applicable to practical problems. • Our CVPR paper imposes regularization on transformation which causes the transformation solution close to the predefined value. To address this issue, we propose a new formulation targeted at 2D/3D similarity registration problems, where regularization on transformation is abandoned in favor of constraints on transformation. This results in an algorithm capable of handling unknown arbitrary similarity transformations. • We conducted extensive experiments on 2D/3D synthetic and real data to test the performance ofthe proposed method. The experimental results demonstrate much better robustness of the proposed method over state-of-the-art methods. Matching partially overlapping point sets is a challenging problem in computer vision. To achieve this goal, we model point matching as a mixed linear assignment - least square problem. By eliminating the transformation variable, we reduce the minimization problem to a concave optimization problem with the property that the objective function can be converted into a form with few nonlinear terms. We then use a heuristic variant of the branch-and-bound algorithm for optimization where convergence of the upper bound is used as the stopping criterion. We also propose a new lower bounding scheme which involves solving a k-cardinality linear assignment problem. Two cases of transformations, transformation output being linear with respect to parameters and 2D/3D similarity transformations, are discussed, resulting in ability to handle unknown arbitrary translation and similarity, respectively. Experimental results demonstrate better robustness of the algorithm over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

• This paper is concerned with solving the parameter estimation problem of PV cells. • An interval branch and bound global optimization algorithm is applied for estimating the unknown PV parameters. • Accuracy of the proposed algorithm is proved against other optimization algorithms. • The performance of two fitness functions, Maximal Absolute Error and Root Mean Square Error, is assessed. In this paper, an interval branch and bound algorithm is proposed to estimate the parameters for three models of photovoltaic (PV) cells. These models are a single diode model (SDM), a double diode model (DDM) and a three diode model (TDM). The minimization of Maximal Absolute Error (MAE) based on the infinite norm is evaluated and compared with the common used objective function called the Root Mean Square Error (RMSE). The MAE aims to minimize the average error on a set of experimental data. In this regard, the parameter estimation is reformatted. The performance of the proposed optimization algorithm is analyzed and tested on all three models. It has good convergence and robust statistical analysis at different operating conditions as well as for various models. The estimated performance characteristics for current-voltage (I - V) and power-voltage (P-V) of the tested cells are very close to the experimental data and compete with existing works in the literature. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a B-spline-based branch-and-bound algorithm for unconstrained global optimization. The key components of the branch-and-bound, a well-known algorithm paradigm for global optimization, are a subdivision scheme and a bound calculation scheme. For these schemes, we first introduce a B-spline hypervolume to approximate an objective function defined in a design space, where the approximation is based on Latin-hypercube sampling points. We then describe a proposed algorithm for finding global solutions approximately within a prescribed tolerance. The algorithm includes two procedures that are performed iteratively until all stopping conditions are satisfied. One involves subdivision into mutually disjoint subspaces and computation of their bound information, both of which are accomplished by using B-spline hypervolumes. The other updates a search tree that represents a hierarchical structure of subdivided subspaces during the solution process. Finally, we examine the computational performance of the proposed algorithm on various test problems that cover most of the difficulties encountered in global optimization. The results show that the proposed algorithm is complete without using heuristics and has good potential for application in large-scale NP-hard optimization. [Copyright &y& Elsevier]

Abstract: In this paper, by solving the relaxed quasiconcave programming problem in outcome space, a new global optimization algorithm for convex multiplicative programming is presented. Two kinds of techniques are employed to establish the algorithm. The first one is outer approximation technique which is applied to shrink relaxation area of quasiconcave programming problem and to compute appropriate feasible points and to raise the capacity of bounding. And the other one is branch and bound technique which is used to guarantee global optimization. Some numerical results are presented to demonstrate the effectiveness and feasibility of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper concerns the application of reformulation techniques in mathematical programming to a specific problem arising in quantum chemistry, namely the solution of Hartree–Fock systems of equations, which describe atomic and molecular electronic wave functions based on the minimization of a functional of the energy. Their traditional solution method does not provide a guarantee of global optimality and its output depends on a provided initial starting point. We formulate this problem as a multi-extremal nonconvex polynomial programming problem, and solve it with a spatial Branch-and-Bound algorithm for global optimization. The lower bounds at each node are provided by reformulating the problem in such a way that its convex relaxation is tight. The validity of the proposed approach was established by successfully computing the ground-state of the helium and beryllium atoms. [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]

In this paper, an expansion scheme for general functions is presented, which can be used to achieve better enclosure of function ranges. In the context of interval branch-and-bound methods for non-smooth global optimization, a pruning technique is given via the expansion. An interval pruning test is established. This pruning test offers the possibility to cut away a large part of the currently investigated box by the optimization algorithm, which can be utilized as an accelerating device similar to the monotonicity test frequently used in interval methods for smooth problems. Numerical computation shows that the proposed method is reliable and can find all solutions of global optimization problem. [Copyright &y& Elsevier]