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Recently, Yamanaka and Yamashita proposed the so-called positively homogeneous optimization problem, which includes many important problems, such as the absolute-value and the gauge optimizations. They presented a closed form of the dual formulation for the problem, and showed weak duality and the equivalence to the Lagrangian dual under some conditions. In this work, we focus on a special positively homogeneous optimization problem, whose objective function and constraints consist of some gauge and linear functions. We prove not only weak duality but also strong duality. We also study necessary and sufficient optimality conditions associated to the problem. Moreover, we give sufficient conditions under which we can recover a primal solution from a Karush-Kuhn-Tucker point of the dual formulation. Finally, we discuss how to extend the above results to general convex optimization problems by considering the so-called perspective functions., Comment: 24 pages

The stochastic variational inequality problem (SVIP) is an equilibrium model that includes random variables and has been widely applied in various fields such as economics and engineering. Expected residual minimization (ERM) is an established model for obtaining a reasonable solution for the SVIP, and its objective function is an expected value of a suitable merit function for the SVIP. However, the ERM is restricted to the case where the distribution is known in advance. We extend the ERM to ensure the attainment of robust solutions for the SVIP under the uncertainty distribution (the extended ERM is referred to as distributionally robust expected residual minimization (DRERM), where the worst-case distribution is derived from the set of probability measures in which the expected value and variance take the same sample mean and variance, respectively). Under suitable assumptions, we demonstrate that the DRERM can be reformulated as a deterministic convex nonlinear semidefinite programming to avoid numerical integration.

In the last two decades, many descent methods for multiobjective optimization problems were proposed. In particular, the steepest descent and the Newton methods were studied for the unconstrained case. In both methods, the search directions are computed by solving convex subproblems, and the stepsizes are obtained by an Armijo-type line search. As a consequence, the objective function values decrease at each iteration of the algorithms. In this work, we consider nonmonotone line searches, i.e., we allow the increase of objective function values in some iterations. Two well-known types of nonmonotone line searches are considered here: the one that takes the maximum of recent function values, and the one that takes their average. We also propose a new nonmonotone technique specifically for multiobjective problems. Under reasonable assumptions, we prove that every accumulation point of the sequence produced by the nonmonotone version of the steepest descent and Newton methods is Pareto critical. Moreover, we present some numerical experiments, showing that the nonmonotone technique is also efficient in the multiobjective case.

Dimethyl trisulfide (DMTS) is the main component of hineka, an off-flavor generated in sake during storage. Genshu, or undiluted sake, is usually diluted with water during warimizu, the process of adjusting the alcohol content of sake. In this study, we evaluated how the inorganic element composition of sake dilution water affects the DMTS-producing potential of the sake (DMTS-pp, determined as the DMTS concentration in sake stored at 70°C for 1 week after dilution) using inductively coupled plasma-mass spectrometry (ICP-MS). Partial least squares (PLS) regression analysis was conducted with the ICP-MS data as the explanatory variable and DMTS-pp as the response variable, and the selection of inorganic elements for the construction of the PLS model was performed using variable importance in projection scores. The findings confirmed that some of the compounds containing the inorganic elements extracted from the PLS regression analysis contribute to DMTS-pp.

The augmented Lagrangian method is a classical solution method for nonlinear optimization problems. At each iteration, it minimizes an augmented Lagrangian function that consists of the constraint functions and the corresponding Lagrange multipliers. If the Lagrange multipliers in the augmented Lagrangian function are close to the exact Lagrange multipliers at an optimal solution, the method converges steadily. Since the conventional augmented Lagrangian method uses inaccurate estimated Lagrange multipliers, it sometimes converges slowly. In this paper, we propose a novel augmented Lagrangian method that allows the augmented Lagrangian function and its minimization problem to have variable constraints at each iteration. This allowance enables the new method to get more accurate estimated Lagrange multipliers by exploiting Karush–Kuhn–Tucker points of the subproblems and consequently to converge more efficiently and steadily.

The alternating direction method of multipliers (ADMM) is an effective method for solving wide fields of convex problems. At each iteration, the classical ADMM solves two subproblems exactly. However, in many applications, it is expensive or impossible to obtain the exact solutions of the subproblems. To overcome the difficulty, some proximal terms are added to the subproblems. This class of methods normally solves the original subproblem approximately, and thus takes more iterations. This fact urges us to consider that a special proximal term can lead to a better result as the classical ADMM. In this paper, we propose a proximal ADMM whose regularized matrix in the proximal term is generated by the BFGS update (or limited memory BFGS) at every iteration. These types of matrices use second-order information of the objective function. The convergence of the proposed method is proved under certain assumptions. Numerical results are presented to show the effectiveness of the proposed proximal ADMM., 17 pages, 5 tables

The limited memory BFGS (L-BFGS) method is one of the popular methods for solving large-scale unconstrained optimization. Since the standard L-BFGS method uses a line search to guarantee its global convergence, it sometimes requires a large number of function evaluations. To overcome the difficulty, we propose a new L-BFGS with a certain regularization technique. We show its global convergence under the usual assumptions. In order to make the method more robust and efficient, we also extend it with several techniques such as nonmonotone technique and simultaneous use of the Wolfe line search. Finally, we present some numerical results for test problems in CUTEst, which show that the proposed method is robust in terms of solving number of problems.

Many descent algorithms for multiobjective optimization have been developed in the last two decades. Tanabe et al. (Comput Optim Appl 72(2):339--361, 2019) proposed a proximal gradient method for multiobjective optimization, which can solve multiobjective problems, whose objective function is the sum of a continuously differentiable function and a closed, proper, and convex one. Under reasonable assumptions, it is known that the accumulation points of the sequences generated by this method are Pareto stationary. However, the convergence rates were not established in that paper. Here, we show global convergence rates for the multiobjective proximal gradient method, matching what is known in scalar optimization. More specifically, by using merit functions to measure the complexity, we present the convergence rates for non-convex ($O(\sqrt{1 / k})$), convex ($O(1 / k)$), and strongly convex ($O(r^k)$ for some $r \in (0, 1)$) problems. We also extend the so-called Polyak-{\L}ojasiewicz (PL) inequality for multiobjective optimization and establish the linear convergence rate for multiobjective problems that satisfy such inequalities ($O(r^k)$ for some $r \in (0, 1)$)., Comment: will appear in Optim. Lett

We propose new descent methods for unconstrained multiobjective optimization problems, where each objective function can be written as the sum of a continuously differentiable function and a proper convex but not necessarily differentiable one. The methods extend the well-known proximal gradient algorithms for scalar-valued nonlinear optimization, which are shown to be efficient for particular problems. Here, we consider two types of algorithms: with and without line searches. Under mild assumptions, we prove that each accumulation point of the sequence generated by these algorithms, if exists, is Pareto stationary. Moreover, we present their applications in constrained multiobjective optimization and robust multiobjective optimization, which is a problem that considers uncertainties. In particular, for the robust case, we show that the subproblems of the proximal gradient algorithms can be seen as quadratic programming, second-order cone programming, or semidefinite programming problems. Considering these cases, we also carry out some numerical experiments, showing the validity of the proposed methods.

We consider an optimization problem with positively homogeneous functions in its objective and constraint functions. Examples of such positively homogeneous functions include the absolute value function and the $p$-norm function, where $p$ is a positive real number. The problem, which is not necessarily convex, extends the absolute value optimization proposed in [O. L. Mangasarian, Absolute value programming, Computational Optimization and Applications 36 (2007) pp. 43-53]. In this work, we propose a dual formulation that, differently from the Lagrangian dual approach, has a closed-form and some interesting properties. In particular, we discuss the relation between the Lagrangian duality and the one proposed here, and give some sufficient conditions under which these dual problems coincide. Finally, we show that some well-known problems, e.g., sum of norms optimization and the group Lasso-type optimization problems, can be reformulated as positively homogeneous optimization problems., 21 pages

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This paper studies a proximal alternating direction method of multipliers (ADMM) with variable metric indefinite proximal terms for linearly constrained convex optimization problems. The proximal ADMM plays an important role in many application areas, since the subproblems of the method are easy to solve. Recently, it is reported that the proximal ADMM with a certain fixed indefinite proximal term is faster than that with a positive semidefinite term, and still has the global convergence property. On the other hand, Gu and Yamashita studied a variable metric semidefinite proximal ADMM whose proximal term is generated by the BFGS update. They reported that a slightly indefinite matrix also makes the algorithm work well in their numerical experiments. Motivated by this fact, we consider a variable metric indefinite proximal ADMM, and give sufficient conditions on the proximal terms for the global convergence. Moreover, we propose a new indefinite proximal term based on the BFGS update which can satisfy the conditions for the global convergence., 21 pages

The first chromogenic substrate for Aspergillus oryzae acid protease, 'HAP-01', was successfully developed after evaluating the substrate specificity of the enzyme. Furthermore, with HAP-01, digestion-triggered chromophore release was employed as a novel chromogenic technique.

Alternating direction methods of multipliers (ADMM) have been well studied and effectively used in various application fields. The classical ADMM must solve two subproblems exactly at each iteration. To overcome the difficulty of computing the exact solution of the subproblems, some proximal terms are added to the subproblems. Recently, {{a special proximal ADMM has been studied}} whose regularized matrix in the proximal term is generated by the BFGS update (or limited memory BFGS) at every iteration for a structured quadratic optimization problem. {{The numerical experiments also showed}} that the numbers of iterations were almost same as those by the exact ADMM. In this paper, we propose such a proximal ADMM for more general convex optimization problems, and extend the proximal term by the Broyden family update. We also show the convergence of the proposed method under standard assumptions.

Radioactive substances were released into the environment after the nuclear accident at the Fukushima Daiichi Nuclear Power Station; this led to the contamination of the soil at Fukushima Prefecture. Mixing of organic matter with soil during plowing is known to influence radiocesium (134Cs and 137Cs) absorption by crops. However, the effect of mixing organic matter polluted by radioactive substances during plowing on radiocesium absorption by plants is not yet known. The aim of this study was to investigate the effect on the radiocesium absorption by komatsuna (Brassica rapa L. var. perviridis) cultivated in a 45-L container containing Andosol (14,300 Bq kg−1) or Gray Lowland soil (33,500 Bq kg−1) mixed with polluted wheat (Triticum aestivum L. Thell.) straw (2080 Bq kg−1). The radiocesium concentration of the plants and the soil and the amount of exchangeable radiocesium in the soil were determined using a germanium semiconductor. The transfer of radiocesium from the soil to plants decreased by 5...

In southern Japan, sweet potato weevils Euscepes postfasciatus (Fairmaire) are being eradicated using the sterile insect technique because of their damaging effects on sweet potato crops. However, the effect of irradiation on the dispersal and survival of this species needs to be evaluated. We observed the dispersal of normal and irradiated weevils for 21 days after their release in a sweet potato field during all four seasons, and estimated their survival using the Weibull function. Normal weevils generally moved further than irradiated weevils, and all weevils had greater dispersal distances in the summer than in the winter, with spring and autumn intermediate between these two extremes (summer: 0.23 m/day versus 0.29 m/day; winter: 0.15 m/day versus 0.07 m/day; spring: 0.20 m/day versus 0.17 m/day; autumn: 0.20 m/day versus 0.15 m/day, respectively). Normal weevils had low variation in mean life expectancy (approximately 8 days throughout the year), whereas the life expectancy of irradiated weevils was drastically reduced in the summer (2.20 days). The implications of these results for the efficiency of this eradication technique are discussed.

In this paper, we propose a class of block coordinate proximal gradient (BCPG) methods for solving large-scale nonsmooth separable optimization problems. The proposed BCPG methods are based on the Bregman functions, which may vary at each iteration. These methods include many well-known optimization methods, such as the quasi-Newton method, the block coordinate descent method, and the proximal point method. For the proposed methods, we establish their global convergence properties when the blocks are selected by the Gauss---Seidel rule. Further, under some additional appropriate assumptions, we show that the convergence rate of the proposed methods is R-linear. We also present numerical results for a new BCPG method with variable kernels for a convex problem with separable simplex constraints.

In this paper, we propose a new exchange method for solving convex semi-infinite programming problems SIPs. The traditional exchange method solves a sequence of finitely relaxed subproblems, that is, subproblems with finitely many constraints chosen from the original constraints. On the other hand, our exchange method solves a sequence of new subproblems, in which the traditional finite subproblems are refined by the quadratic approximation. Under mild assumptions, the refined subproblems approximate the original SIP more precisely than the traditional subproblems. Moreover, although those subproblems are still SIPs, they can be solved efficiently by reformulating them as certain optimization problems with finitely many constraints. We establish the global convergence property of the proposed algorithm. Finally, we examine the efficiency of the algorithm by some numerical experiments.

In this paper, we study the iteration complexity of a block coordinate gradient descent (BCGD) method with a cyclic rule for solving convex optimization problems. We propose a new Lipschitz continuity-like assumption and show that the iteration complexity for the proposed BCGD method can be improved to $O(\frac{\max\{M, \;{L}\}}{\varepsilon})$, where $M$ is the constant in the proposed assumption, ${L}$ is the usual Lipschitz constant for the gradient of the objective function, and $\varepsilon>0$ is the required precision. In addition, we analyze the relation between $M$ and ${L}$, and prove that, in the worst case, $M\leq \sqrt{N}{L}$, where $N$ is the number of blocks.

In this paper, we propose a regularized Newton method without line search. The proposed method controls a regularization parameter instead of a step size in order to guarantee the global convergence. We show that the proposed algorithm has the following convergence properties. (a) The proposed algorithm has global convergence under appropriate conditions. (b) It has superlinear rate of convergence under the local error bound condition. (c) An upper bound of the number of iterations required to obtain an approximate solution $$x$$x satisfying $$\Vert \nabla f(x) \Vert \le \varepsilon $$??f(x)?≤? is $$O(\varepsilon ^{-2})$$O(?-2), where $$f$$f is the objective function and $$\varepsilon $$? is a given positive constant.

Based on the idea of maximum determinant positive definite matrix completion, Yamashita (Math Prog 115(1):1–30, 2008) proposed a new sparse quasi-Newton update, called MCQN, for unconstrained optimization problems with sparse Hessian structures. In exchange of the relaxation of the secant equation, the MCQN update avoids solving difficult subproblems and overcomes the ill-conditioning of approximate Hessian matrices. However, local and superlinear convergence results were only established for the MCQN update with the DFP method. In this paper, we extend the convergence result to the MCQN update with the whole Broyden’s convex family. Numerical results are also reported, which suggest some efficient ways of choosing the parameter in the MCQN update the Broyden’s family.

In this paper, we propose a primal-dual interior point method for nonlinear semidenite pro- gramming problems and show its superlinear convergence. This method is based on generalized shifted barrier Karush-Kuhn-Tuck er (KKT) conditions, which include barrier KKT conditions and shifted barrier KKT conditions as a special case. This method solves two Newton equations in a single iteration to guaran- tee superlinear convergence. We replace the coefficient matrix of the second Newton equation with that of therst to reduce the computational time of the single iteration. We show that the superlinear convergence of the proposed method with the replacement under the usual assumptions.

We investigate a global complexity bound of the Levenberg–Marquardt Method (LMM) for nonsmooth equations. The global complexity bound is an upper bound to the number of iterations required to get an approximate solution that satisfies a certain condition. We give sufficient conditions under which the bound of the LMM for nonsmooth equations is the same as smooth cases. We also show that it can be reduced under some regularity assumption. Furthermore, by applying these results to nonsmooth equations equivalent to the nonlinear complementarity problem (NCP), we get global complexity bounds for the NCP. In particular, we give a reasonable bound when the mapping involved in the NCP is a uniformly P-function.

In this paper, we briefly review the extensions of quasi-Newton methods for large-scale optimization. Specially, based on the idea of maximum determinant positive definite matrix completion, Yamashita (2008) proposed a new sparse quasi-Newton update, called MCQN, for unconstrained optimization problems with sparse Hessian structures. In exchange of the relaxation of the secant equation, the MCQN update avoids solving difficult subproblems and overcomes the ill-conditioning of approximate Hessian matrices. A global convergence analysis is given in this paper for the MCQN update with Broyden's convex family assuming that the objective function is uniformly convex and its dimension is only two. &nbsp This paper is dedicated to Professor Masao Fukushima on occasion of his 60th birthday.

In this paper, we consider the unconstrained optimization problem under the following conditions: (S1) The objective function is evaluated with a certain bounded error, (S2) the error is controllable, that is, the objective function can be evaluated to any desired accuracy, and (S3) more accurate evaluation requires a greater computation time. This situation arises in many fields such as engineering and financial problems, where objective function values are obtained from considerable numerical calculation or a simulation. Under (S2) and (S3), it seems reasonable to set the accuracy of the evaluation to be low at points far from a solution, and high at points in the neighborhood of a solution. In this paper, we propose a derivative-free trust-region algorithm based on this idea. For this purpose, we consider (i) how to construct a quadratic model function by exploiting pointwise errors and (ii) how to control the accuracy of function evaluations to reduce the total computation time of the algorithm. For (i), we propose a method based on support vector regression. For (ii), we present an updating formula of the accuracy of which is related to the trust-region radius. We present numerical results for several test problems taken from CUTEr and a financial problem of estimating implied volatilities from option prices.

In this paper, we investigate a global complexity bound of the Levenberg-Marquardt method (LMM) for the nonlinear least squares problem. The global complexity bound for an iterative method solving unconstrained minimization of φ is an upper bound to the number of iterations required to get an approximate solution, such that ‖∇φ(x)‖≤e. We show that the global complexity bound of the LMM is O(e −2).

The unit commitment problem (UCP) for an electric power system is used to determine the schedules of power units that minimize the total production cost over a planning horizon while satisfying the load demand, spinning reserve, and operating constraints of individual units. When the number of units is large and the planning horizon is long, the UCP is a large-scale problem, for which an exact optimal solution is difficult to obtain within a reasonable computation time. The Lagrangian relaxation (LR) method is known to be useful for large-scale UCPs. The LR method first solves the dual problem of the UCP, and then constructs a feasible solution from the dual solution by using some heuristics. In this paper, we propose new local search (LS) methods for improving the feasible solution obtained by the LR method. We define the neighborhood of the local search as the feasible set in which the on-off states of all but one or two units are fixed. The neighborhood search can then be executed by solving the one unit or two UCPs, which are efficiently solved by dynamic programming if no ramp-rate limit constraint exists. Numerical results show that the proposed LS methods can find feasible schedules for which the costs are lower than those obtained by the existing methods. The applicability of the proposed methods to long-term UCPs is also demonstrated.

The regularized Newton method (RNM) is one of the efficient solution methods for the unconstrained convex optimization. It is well-known that the RNM has good convergence properties as compared to the steepest descent method and the pure Newton’s method. For example, Li, Fukushima, Qi and Yamashita showed that the RNM has a quadratic rate of convergence under the local error bound condition. Recently, Polyak showed that the global complexity bound of the RNM, which is the first iteration k such that ‖∇f(xk)‖≤e, is O(e−4), where f is the objective function and e is a given positive constant. In this paper, we consider a RNM extended to the unconstrained “nonconvex” optimization. We show that the extended RNM (E-RNM) has the following properties. (a) The E-RNM has a global convergence property under appropriate conditions. (b) The global complexity bound of the E-RNM is O(e−2) if ∇2f is Lipschitz continuous on a certain compact set. (c) The E-RNM has a superlinear rate of convergence under the local error bound condition.

大豆のリビングマルチ栽培において，マルチとして利用される小麦や大麦が，生育初期の大豆の根系形成にどのように影響するかを染色法により検討した．大麦をマルチとして想定した処理区では，大豆のみを栽培した処理区と比較して，大豆の地上部乾物重，総根長，総根重ともに抑制された．小麦をマルチとして想定した処理区では，大豆の地上部乾物重は，リビングマルチの影響を受けておらず，総根長および総根重のみが抑制されていた．また，小麦に比べて大麦の方が，より大豆の根域に侵入していることが示され，リビングマルチによって大豆の根系拡大が抑制されることが明らかになった．大豆の根系形成がリビングマルチの影響を受ける一方で，麦類の根系形成は隣接作物の影響を受けないことが示された．これらの結果から，麦類を利用したリビングマルチ栽培において播種直後から地下部では競合関係にあり，大麦が大豆の根域に侵入し，より強く大豆の生育を抑制していると考えられた．

Road pricing is considered one of the effective means to reduce traffic congestion and environmental damage, and it has been introduced in major highways of most countries. The road pricing problem can be formulated as a mathematical program with equilibrium constraints (MPEC) and the resulting MPEC can be solved efficiently by the implicit programming approach if the user's route costs are additive. However, route costs are generally nonadditive in the real world. In this paper we consider road pricing on the traffic equilibrium problem with nonadditive route costs based on users' disutility functions. We then show that this formulation can be reformulated as a mathematical program with strictly monotone mixed complementarity problem (MCP). Since a strictly monotone MCP has a unique solution for each upper level variable, we can apply the implicit programming approach to solve the resulting reformulation. We establish the differentiability of the resulting implicit function. Numerical experiments using various disutility functions and sample networks are done, and the results show that the implicit programming approach is robust to find a solution of the road pricing problem.

Various models of tra-c equilibrium problems (TEPs) with nonadditive route costs have been proposed in the last decade. However, equilibria of those models are not easy to obtain because the variational inequality problems (VIPs) derived from those models are not monotone in general. In this paper, we consider a TEP whose route cost functions are nonadditive disutility functions of time (with money converted to time). We show that the TEP with the disutility functions can be reformulated as a monotone Mixed Complementarity Problem (MCP) under appropriate conditions. We then establish the existence and uniqueness results for an equilibrium of the TEP. Numerical experiments are carried out using various sample networks with difierent disutility functions for both the single-mode case and the case of two difierent transportation modes in the network.

Quasi-Newton methods are powerful techniques for solving unconstrained minimization problems. Variable metric methods, which include the BFGS and DFP methods, generate dense positive definite approximations and, therefore, are not applicable to large-scale problems. To overcome this difficulty, a sparse quasi-Newton update with positive definite matrix completion that exploits the sparsity pattern $$E :=\{(i, j)\;|\; (\nabla^2 f(x))_{ij} \neq 0\,{\rm for\,some}\, x \in R^n\}$$ of the Hessian is proposed. The proposed method first calculates a partial approximate Hessian $$H^{QN}_{ij}, (i, j) \in F$$, where $$F \supseteq E$$, using an existing quasi-Newton update formula such as the BFGS or DFP methods. Next, a full matrix H k+1, which is a maximum-determinant positive definite matrix completion of $$H^{QN}_{ij}, (i, j) \in F$$, is obtained. If the sparsity pattern E (or its extension F) has a property related to a chordal graph, then the matrix H k+1 can be expressed as products of some sparse matrices. The time and space requirements of the proposed method are lower than those of the BFGS or the DFP methods. In particular, when the Hessian matrix is tridiagonal, the complexities become O(n). The proposed method is shown to have superlinear convergence under the usual assumptions.

Recently, the risk that garbages in space (space debris) conflict with a running space satellite or fall to the ground is increasing. To prevent the accident beforehand the Japan Aerospace Exploration Agency observes the space debris by a single radar whose operation plan is obtained by a heuristic technique. However, since the technique does not use global information of a prediction of the space debris orbit, the plan is far from the optimum. In this paper we propose a new technique using the global information. The method obtains an ordering of an observation of the debris on the basis of the longest path of a graph whose nodes corresponds to the debris. The number of nodes of the longest path provides an upper bound of the optimum. We experimented the proposed technique for actual prediction data. The results showed that the proposed technique can make a plan that observes twice the space debris than those of the existing technique, and that the differences from the upper bound are 0 or 1.

Effects of the antiparasitic drug ivermectin on the dung-breeding flies and beetles Liatongus minutus (Motschulsky) were studied in laboratory and field experiments in Hokkaido, Japan. Ivermectin was detected in dung from 1 to 21 d after treatment, with a peak at the first day after treatment in two pour-on administrations (500 μg/kg). Laboratory bioassays were performed on the flies Musca bezzii Patton and Cragg and Scatophaga stercoraria L. and on the beetle Liatongus minutus. Dung from treated cattle inhibited larval development of M. bezzii from 1 to 14 d and pupation rate was reduced 21 d after treatment. In S. stercoraria, pupation and emergence rates were reduced for up to 14 and 28 d, respectively. In laboratory experiments of the dung beetle L. minutus, no significant difference was found in numbers of brood balls constructed per female between dung from treated and control cattle, whereas in field experiments, numbers of brood balls recovered in treatment were more abundant than that of...

application/pdf, The effects of antiparasitic drug, ivermectin, on the dung-breeding flies were studied in laboratory and field experiments in Hokkaido, Japan. In two pour-on treatments (500μg/kg), ivermectin was excreted in dung for up to 14 and 21 days after treatment, with peaks at 3 days and 1 day, respectively. Dung from treated cattle prevented the larval development of Haematobia irritans and Neomyia cornicina up to 14 days and reduced the larval and pupal survival rates at 21 days after treatment. In the field experiment using emergence traps, the numbers of emerged flies from dung pats were 3,655 (18 families) in control dung and 2,234 (16 families) in treated dung. Especially, Musca bezzii, Ravinia striata, Sepsis duplicata, Sepsis thoracica, Sepsis cynipsea, Sphaeroceridea, Empididae, Sciaridae and Chironomidae were severely reduced in treated dung. Reduction of cyclorrhaphaous flies similarly occurred at 1, 3 and 7 days after treatment, which coincides with high concentrations of ivermectin. Conversely, Ceratopogonidae and Phoridae increased in treated dung, regardless of days (1, 3 and 7) after treatment. Dry weights of flies emerged from dung pats of treated cattle in the field experiment were only 5.8% of those from dung of control cattle, indicating that dung-decomposing activity by fly larvae was supressed in dung of treated cattle.

The second-order cone complementarity problem (SOCCP) is a wide class of problems containing the nonlinear complementarity problem (NCP) and the second-order cone programming problem (SOCP). Recently, Fukushima, Luo, and Tseng [SIAM J. Optim., 12 (2001), pp. 436--460] extended some merit functions and their smoothing functions for NCP to SOCCP. Moreover, they derived computable formulas for the Jacobians of the smoothing functions and gave conditions for the Jacobians to be invertible. In this paper, we propose a globally and quadratically convergent algorithm, which is based on smoothing and regularization methods, for solving monotone SOCCP. In particular, we study strong semismoothness and Jacobian consistency, which play an important role in establishing quadratic convergence of the algorithm. Furthermore, we examine the effectiveness of the algorithm by means of numerical experiments.

In this article, we formulate the problem of multiuser power control for digital subscriber lines (DSL) as a nonlinear complementarity problem (NCP). We study conditions under which the resulting NCP belongs to the class P 0 and its solution is B-regular. The NCP formulation makes it possible to use the Newton-type smoothing methods (SMs) to efficiently compute a Nash equilibrium solution. In our computer simulations, the SM appears much more robust to the presence of strong interference than the existing synchronous water-filling method. We also present an extension of the NCP formulation, which can lead to substantial increase in the rate sum performance of the DSL system. Part of this research was performed while the author was with the Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario L8S 4K1, Canada. This research was performed while this author was visiting McMaster University, Canada.

This paper studies convergence properties of regularized Newton methods for minimizing a convex function whose Hessian matrix may be singular everywhere. We show that if the objective function is LC2, then the methods possess local quadratic convergence under a local error bound condition without the requirement of isolated nonsingular solutions. By using a backtracking line search, we globalize an inexact regularized Newton method. We show that the unit stepsize is accepted eventually. Limited numerical experiments are presented, which show the practical advantage of the method.

In this paper we focus on the problem of identifying the index sets P(x):={i|xi>0}, N(x):={i|Fi(x)>0} and C(x):={i|xi=Fi(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.

Mureka-non-forming sake koji molds were constructed from an Aspergillus oryzae industrial strain by the disruption of the mreA gene using a host-vector system with the ptrA gene as a dominant selectable marker. All of the mreA gene disruptants obtained retained the advantages of the host strain in terms of the brewing characteristics, while their isoamyl alcohol oxidase (IAAOD) activities were significantly lower than that of the host strain. Sake brewing was successfully carried out using the koji prepared with the disruptants, followed by storage of the resultant non-pasteurized sake (nama-shu). The isovaleraldehyde (i-Val) concentration in the sake brewed the host strain increased rapidly and reached the threshold values for mureka, 1.8 ppm and 2.6 ppm after storage at 20 degrees C for 42 d and 63 d, respectively, while those of the disruptants were less than 0.5 ppm even after storage at 20 degrees C or 30 degrees C for 63 d. In the sensory evaluation of the sake stored at 20 degrees C or 30 degrees C for 63 d, all members of the panel recognized the strong mureka flavor of the sake brewed with the host strain, while they did not detect this flavor in the sake brewed with the disruptants. Thus, we concluded that the mreA gene disruptants can be used for the production of sake in which mureka is not formed.

In this paper, we consider the Extended Kalman Filter (EKF) for solving nonlinear least squares problems. EKF is an incremental iterative method based on Gauss-Newton method that has nice convergence properties. Although EKF has the global convergence property under some conditions, the convergence rate is only sublinear under the same conditions. One of the reasons why EKF shows slow convergence is the lack of explicit stepsize. In the paper, we propose a stepsize rule for EKF and establish global convergence of the algorithm under the boundedness of the generated sequence and appropriate assumptions on the objective function. A notable feature of the stepsize rule is that the stepsize is kept greater than or equal to 1 at each iteration, and increases at a linear rate of k under an additional condition. Therefore, we can expect that the proposed method converges faster than the original EKF. We report some numerical results, which demonstrate that the proposed method is promising.

The purpose of this paper is to present an algorithm for solving the monotone nonlinear complementarity problem (NCP) that enjoys superlinear convergence in a genuine sense without the uniqueness and nondegeneracy conditions. Recently, Yamashita and Fukushima (2001) proposed a method based on the proximal point algorithm (PPA) for monotone NCP. The method has the favorable property that a generated sequence converges to the solution set of NCP superlinearly. However, when a generated sequence converges to a degenerate solution, the subproblems may become computationally expensive and the method does not have genuine superlinear convergence. More recently, Yamashita et al. (2001) presented a technique to identify whether a solution is degenerate or not. Using this technique, we construct a differentiable system of nonlinear equations in which the solution is a solution of the original NCP. Moreover, we propose a hybrid algorithm that is based on the PPA and uses this system. We show that the proposed algorithm has a genuine quadratic or superlinear rate of convergence even if it converges to a solution that is neither unique nor nondegenerate.

In this paper, we consider convergence properties of the Levenberg-Marquardt method for solving nonlinear equations. It is well-known that the nonsingularity of Jacobian at a solution guarantees that the Levenberg-Marquardt method has a quadratic rate of convergence. Recently, Yamashita and Fukushima showed that the Levenberg-Marquardt method has a quadratic rate of convergence under the local error bound assumption, which is milder than the nonsingularity of Jacobian. In this paper, we show that the inexact Levenberg-Marquardt method (ILMM), which does not require computing exact search directions, has a superlinear rate of convergence under the same local error bound assumption. Moreover, we propose the ILMM with Armijo's stepsize rule that has global convergence under mild conditions.

We have found a gene (thiP) encoding thiamine pyrophosphokinase (TPK) in the Aspergillus oryzae genome. No riboswitch-like region was found in the upstream region of thiP, although it was repressed probably by thiamine pyrophosphate (TPP) as well as thiA and nmtA, which are strictly regulated by TPP-riboswitch sequence. To improve the productivity of TPP in A. oryzae, we constructed the strain in which thiA, nmtA and thiP were overexpressed simultaneously. The resulting strain accumulated intracellular TPP 4-fold higher than did the control strain.