a discrete dynamic convexized method for nonlinear integer programming in this paper we consider the box constrained nonlinear integer programming problem we present an auxiliary function which has the same discrete global minimizers as the problem the minimization of the function using a discrete local search method can escape successfully from previously converged discrete local minimizers by taking increasing values of a parameter we propose an algorithm to find a global minimizer of the box constrained nonlinear integer programming problem the algorithm minimizes the auxiliary function from random initial points we prove that the algorithm can converge asymptotically with probability one numerical experiments on a set of test problems show that the algorithm is efficient and robust

a filled function method for finding a global minimizer on global integer optimization the paper gives a definition of the filled function for nonlinear integer programming this definition is modified from that of the global convexized filled function for continuous global optimization a filled function with only one parameter which satisfies this definition is presented we also discuss the properties of the proposed function and give a filled function method to solve the nonlinear integer programming problem the implementation of the algorithm on several test problems is reported with satisfactory numerical results

recent developments and trends in global optimization many optimization problems in engineering and science require solutions that are globally optimal these optimization problems are characterized by the nonconvexity of the feasible domain or the objective function and may involve continuous and or discrete variables in this paper we highlight some recent results and discuss current research trends on deterministic and stochastic global optimization and global continuous approaches to discrete optimization

finding global minimizer with one parameter filled function on unconstrained global optimization abstract in this paper a filled function with one parameter is proposed for solving unconstrained global optimization problems this filled function is modified from the previously reported one see paper y j yang y l shang a new filled function method for unconstrained global optimization applied mathematics and computations 173 1 2006 501 512 the properties of the filled function are discussed in this paper an algorithm for unconstrained global optimization is developed from this new filled function the computational results show that this algorithm is efficient and reliable

on the geometry of non holonomic lagrangian systems we present a geometric framework for non holonomic lagrangian systems in terms of distributions on the configuration manifold if the constrained system is regular an almost product structure on the phase space of velocities is constructed such that the constrained dynamics is obtained by projecting the free dynamics if the constrained system is singular we develop a constraint algorithm which is very similar to that developed by dirac and bergmann and later globalized by gotay and nester special attention to the case of constrained systems given by connections is paid in particular we extend the results of koiller for caplygin systems an application to the so called non holonomic geometry is given

a revised cut peak function method for box constrained continuous global optimization in this paper we modify the concept of cut peak function given in wang et al y wang w fang t wu a deterministic algorithm of global optimization using cut peak functions technique report in the conference of mathematical programming of china 2006 and then propose a revised cut peak function algorithm for solving box constrained continuous optimization problems the smoothing technique is used to overcome the difficulty arising from the non smoothness of the constructed function by using the exterior penalty function method we find iteratively a better minimizer from the current local minimizer till a global minimizer of the concerned problem is found some preliminary numerical results are reported

a filled function method for finding a global minimizer of a function of several variables the concept of a filled function is introduced we construct a particular filled function and analyze its properties an algorithm for global minimization is generated based on the concept and properties of the filled function some typical examples with 1 to 10 variables are tested and computational results show that in most cases this algorithm works better than the tunneling algorithm the advantages and disadvantages are analyzed and further research directions are discussed

a class of generalized filled functions with improved computability the filled function method ffm is an approach to find the global minimum of multimodal functions the computability of conventional filled functions is limited as they are defined on either exponential or logarithmic terms this paper proposes a new filled function that does not have such disadvantages numerical experiments on typical testing functions showed that the new function is superior to the conventional one

bayesian sequential estimation of the reliability of a parallel series system we give a risk averse solution to the problem of estimating the reliability of a parallel series system we adopt a beta binomial model for components reliabilities assuming that the total sample size for the experiment is fixed the allocation at subsystems or components level may be random based on the sampling schemes for parallel and series systems separately we propose a hybrid sequential scheme for the parallel series system asymptotic optimality of the bayes risk associated with quadratic loss is proved with the help of martingale convergence properties a comparison is given with the best fixed design with numerical examples

on representations and integrability of mathematical structures in energy conserving physical systems in the present paper we elaborate on the underlying hamiltonian structure of interconnected energy conserving physical systems it is shown that a power conserving interconnection of port controlled generalized hamiltonian systems leads to an implicit generalized hamiltonian system and a power conserving partial interconnection to an implicit port controlled hamiltonian system the crucial concept is the notion of a generalized dirac structure defined on the space of energy variables or on the product of the space of energy variables and the space of flow variables in the port controlled case three natural representations of generalized dirac structures are treated necessary and sufficient conditions for closedness or integrability of dirac structures in all three representations are obtained the theory is applied to implicit port controlled generalized hamiltonian systems and it is shown that the closedness condition for the dirac structure leads to strong conditions on the input vector fields

a discrete filled function algorithm embedded with continuous approximation for solving max cut problems in this paper a discrete filled function algorithm embedded with continuous approximation is proposed to solve max cut problems a new discrete filled function is defined for max cut problems and properties of the function are studied in the process of finding an approximation to the global solution of a max cut problem a continuation optimization algorithm is employed to find local solutions of a continuous relaxation of the max cut problem and then global searches are performed by minimizing the proposed filled function unlike general filled function methods characteristics of max cut problems are used the parameters in the proposed filled function need not to be adjusted and are exactly the same for all max cut problems that greatly increases the efficiency of the filled function method numerical results and comparisons on some well known max cut test problems show that the proposed algorithm is efficient to get approximate global solutions of max cut problems

hamilton jacobi theory for degenerate lagrangian systems with holonomic and nonholonomic constraints we extend hamilton jacobi theory to lagrange dirac or implicit lagrangian systems a generalized formulation of lagrangian mechanics that can incorporate degenerate lagrangians as well as holonomic and nonholonomic constraints we refer to the generalized hamilton jacobi equation as the dirac hamilton jacobi equation for non degenerate lagrangian systems with nonholonomic constraints the theory specializes to the recently developed nonholonomic hamilton jacobi theory we are particularly interested in applications to a certain class of degenerate nonholonomic lagrangian systems with symmetries which we refer to as weakly degenerate chaplygin systems that arise as simplified models of nonholonomic mechanical systems these systems are shown to reduce to non degenerate almost hamiltonian systems i e generalized hamiltonian systems defined with non closed two forms accordingly the dirac hamilton jacobi equation reduces to a variant of the nonholonomic hamilton jacobi equation associated with the reduced system we illustrate through a few examples how the dirac hamilton jacobi equation can be used to exactly integrate the equations of motion

finding discrete global minima with a filled function for integer programming the filled function method is an approach to find the global minimum of multidimensional functions this paper proposes a new definition of the filled function for integer programming problem a filled function which satisfies this definition is presented furthermore we discuss the properties of the filled function and design a new filled function algorithm numerical experiments on several test problems with up to 50 integer variables have demonstrated the applicability and efficiency of the proposed method

a critical review of discrete filled function methods in solving nonlinear discrete optimization problems many real life problems can be modeled as nonlinear discrete optimization problems such problems often have multiple local minima and thus require global optimization methods due to high complexity of these problems heuristic based global optimization techniques are usually required when solving large scale discrete optimization or mixed discrete optimization problems one of the more recent global optimization tools is known as the discrete filled function method nine variations of the discrete filled function method in literature are identified and a review on theoretical properties of each method is given some of the most promising filled functions are tested on various benchmark problems numerical results are given for comparison

the globally convexized filled functions for global optimization a new filled function the globally convexized filled function is proposed the value of this function tends to positive infinity as the norm of the variable vector tends to infinity and it has no stationary point in the region in which the objective function value is greater than or equal to the least value found so far but it does have a minimizer not only along the radius direction from the minimizer with the least objective function value found so far like filled function found earlier by ge in the region in which the objective function value is less than the least value found so far but with a prefixed minimizer how to adjust parameters in the filled function is considered such a filled function can be appropriately combined with stochastic stopping rules proposed by boender rinnooy kan and timmer the computational results show that this algorithm is quite efficient and reliable

a new discrete filled function method for finding global minimizer of the integer programming in this paper a new discrete filled function method is proposed for finding a global minimizer of integer programming problems only one parameter is included in the proposed filled function and it does not need to be adjusted further when it is taken as large as possible moreover the current local minimizer obtained by minimizing the proposed filled function will be one of the local minimizers of the original problem and it is better than the minimizers found previously thus it is not necessary to use a local search method to the original function as a result the computation cost of the proposed discrete filled function method is relatively low numerical results demonstrate the effectiveness of the proposed method

a continuous approach to nonlinear integer programming this paper is concerned with nonlinear integer programming problems unconstrained and constrained as well as mixed the problems are transformed into nonlinear global optimization problems and then solved by the filled function transformation method this approach should be efficient since it has been shown that the filled function transformation method is efficient in solving global optimization problems with large numbers up to 30 2 5 in the present examples of local minimizers however the sense of efficient as having polynomial complexity in the worst or average case is not suitable for nonlinear integer programming problems since the complexity of a nonlinear programming algorithm is in general nonpolynomial

a discrete filled function algorithm for approximate global solutions of max cut problems a discrete filled function algorithm is proposed for approximate global solutions of max cut problems a new discrete filled function is defined for max cut problems and the properties of the filled function are studied unlike general filled function methods using the characteristic of max cut problems the parameters in proposed filled function need not be adjusted this greatly increases the efficiency of the filled function method by combining a procedure that randomly generates initial points for minimization of the filled function the proposed algorithm can greatly reduce the calculation cost and be applied to large scale max cut problems numerical results on different sizes and densities test problems indicate that the proposed algorithm is efficient and stable to get approximate global solutions of max cut problems

an approximate algorithm for nonlinear integer programming this paper presents an approximate algorithm which is modified from the filled function method for continuous global optimization to solve nonlinear integer programming problems unlike the other approximate methods the algorithm tries to improve a discrete local minimal solution by minimizing a filled function it is a direct method numerical experiments show that this algorithm is efficient

reduction of constrained systems with symmetries a general model is proposed for constrained dynamical systems on a symplectic manifold which covers among others the description of lagrangian and hamiltonian systems with nonholonomic constraints and the canonical description of mechanical systems with a singular lagrangian the reduction properties of these systems in the presence of symmetry are investigated within this general framework