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With the development of modern science and technology, the field of UAV has also entered the era of high-tech exploration. Among them, the task planning, allocation, path exploration, and algorithm optimization of heterogeneous multi UAV technology are our main concerns. Based on the above situation, this paper proposes a heterogeneous multi UAV task planning technology based on ant colony algorithm powered BP neural network. The planning, research, and design are mainly carried out according to the actual situation of the UAV flight test, and the mathematical programming model is established according to the UAV load degree and maximum flight distance as constraints. This paper focuses on the contribution of the ant colony optimization algorithm to benefit maximization and task minimization. The experimental results show that the BP neural network optimized by the ant colony algorithm can improve the number of iterations and training time. Compared with some comparative algorithms, its performance is better. [ABSTRACT FROM AUTHOR]

Timetable optimization techniques offer opportunity for saving energy and hence reducing operational costs for high-speed rail services. The existing energy-saving timetable optimization is mainly concentrated on the train running state adjustment and the running time redistribution between two stations. Not only the adjustment space of timetables is limited, but also it is hard for the train to reach the optimized running state in reality, and it is difficult to get feasible timetable with running time redistribution between two stations for energy-saving. This paper presents a high-speed railway energy-saving timetable based on stop schedule optimization. Under the constraints of safety interval and stop rate, with the objective of minimizing the increasing energy consumption of train stops and the shortest travel time of trains, the high-speed railway energy-saving timetable optimization model is established. The fuzzy mathematics programming method is used to design an efficient algorithm. The proposed model and algorithm are demonstrated in the actual operation data of Beijing-Shanghai high-speed railway. The results show that the total operating energy consumption of the train is reduced by 3.7%, and the total travel time of the train is reduced by 11 minutes. [ABSTRACT FROM AUTHOR]

In the emerging modern technology of additive manufacturing, the need for optimization can be found in literature in many places. Additive manufacturing (AM) is making an object layer by layer directly from digital data. Previous works of literature have classified additive manufacturing processes into seven types. However, there is a lack of comprehensive review describing the optimization challenges and opportunities in the material extrusion process (polymer technology) and also the need for FDM polymer materials application in impeller making. In this review paper, a specific optimization method called multicriteria decision-making (MCDM) from the mathematical programming technique used in additive manufacturing polymer technology (AMPT) is discussed. The other topics such as different types of optimization techniques, applications of different MCDM tools and their applications in different fields including AM, and the optimization challenges and opportunities in AMPT particularly impeller application are discussed. [ABSTRACT FROM AUTHOR]

Multiple sources localization based on time difference of arrival (TDOA) measurements is investigated in this paper. Different from the traditional methods, a novel and practical multisource localization algorithm is proposed by adopting a priori information of relative distance among emitting sources. Since the maximum likelihood (ML) cost function for multisource estimation is highly nonconvex, the semidefinite relaxation (SDR) is utilized to reformulate the ML cost function. A robust estimator is obtained, which can be solved by semidefinite programming (SDP). Moreover, the constrained Cramér-Rao bound is also derived as a benchmark by considering the range constraints between sources. Simulation results verify the superior performance of the proposed algorithm over the traditional methods. [ABSTRACT FROM AUTHOR]

This paper studies the energy efficiency optimization problem for coordinated multipoint (CoMP)-enabled and backhaul-constrained ultra-dense small-cell networks (UDNs). Energy efficiency is an eternal topic for future wireless communication networks; however, taking actual bottleneck of the backhaul link and the coordinated network architecture into consideration, it is difficult to find an effective way to improve the energy efficiency of the network. Aiming at this problem, we propose to combine cell association, subchannel allocation, backhaul resource allocation, and sleep/on of the cells together to develop an optimization algorithm for energy efficiency in UDN and then solve the formulated energy efficiency optimization problem by means of improved modified particle swarm optimization (IMPSO) and linear programming in mathematics. Simulation results indicate that nearly 13 % energy cost saving and 21 % energy efficiency improvement can be obtained by combining IMPSO with linear programming, and the backhaul link data rate can be improved by 30 % as the number of small cells increases. From the results, it can be found that by combining IMPSO with linear programming, the proposed algorithm can improve the network energy efficiency effectively at the expense of limited complexity. [ABSTRACT FROM AUTHOR]

The passenger transport demands at a given junction station fluctuate obviously in different time periods, which makes the rail departments unable to establish an even train operation schedule. This paper considers an optimization problem for train operations at the junction station in passenger dedicated lines. A satisfaction function of passengers is constructed by means of analyzing the satisfaction characteristics and correlative influencing factors. Through discussing the passengers' travel choice behavior, we formulate an optimization model based on maximum passenger satisfaction for the junction and then design a heuristic algorithm. Finally, a numerical example is provided to demonstrate the application of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce some generalized contractions and prove certain new fixed point results for self-mappings satisfying these contractions in the setting of F -metric space. As an application of our results, we investigate the problem of dynamic programming related to the multistage process which formulates the problems of computer programming and mathematical optimization. We also provide an example to support the validity of our main results. [ABSTRACT FROM AUTHOR]

This paper presents a multi-objective mathematical programming (MMP) model to day-ahead market clearing of joint energy and reserves auctions by integrating a thyristor-controlled series compensator (TCSC) device with the optimization problem developed under normal and contingency cases. The proposed market clearing framework includes minimization of energy and reserves offer cost, congestion rent, TCSC cost, expected interruption cost, line overload, voltage deviation, and loadability limit. A new index called congestion efficiency index is proposed for the best placement of TCSC under network contingency conditions. Traditional MMP methods such as direction scalarization and ε-constraint methods scalarize the objective vector into a single objective. Those cases are time-consuming and require a number of runs equal to the number of desired efficient solutions. In this paper, the non-dominated sorting genetic algorithm II (NSGA-II), which is integrated with an adaptive neuro-fuzzy inference system (ANFIS), is proposed to find the solution of the optimal schedule of the units energy and reserves by which the parameters of NSGA-II (probabilities of crossover and mutation) are dynamically set, according to a training process. The proposed methodology is developed on the IEEE 30-bus test system, and the results are compared with fuzzy-based and ordinary NSGA-II methods. These comparisons confirm the efficiency of the developed method. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Paknejad et al.'s model is considered in this paper. Itemwise multiobjective models for both exponential and uniform lead-time demand are taken and the results are compared numerically both in fuzzy optimization and intuitionistic fuzzy optimization techniques. Objective of this paper is to establish that intuitionistic fuzzy optimizaion method is better than usual fuzzy optimization technique as expected annual cost of this inventory model is more minimized in case of intuitionistic fuzzy optimization method. As a single objective stochastic inventory model where the lead-time demand follows normal distribution andwith varying defective rate, expected annual cost is also measured. Finally the model considers for fuzzy cost components, which make the model more realistic, and numerical values for uniform, exponential, and normal leadtime demand are compared. Necessary graphical presentations are also given besides numerical illustrations. [ABSTRACT FROM AUTHOR]

An introduction is presented in which discusses articles within the issue on topics including local search and mathematical programming; enhancing optimization problems by integrating an Ant algorithm; and migrating birds optimization when solving machine-part cell formation problems.

SUMMARY Modern heuristic optimization algorithms have gained considerable attention in different research fields due to their conceptual simplicity and their ability to deal with different complex optimization problems. Motivated by promising results from the application of these emerging tools on other power system optimization problems, this paper presents a comparative study on the capabilities of three heuristic optimization algorithms for solving the problem of optimal dynamic centralized transmission expansion planning (CTEP). Among the studied algorithms are: Evolutionary particle swarm optimization, differential evolution, and a newly developed tool named mean-variance mapping optimization. Considering a predefined indicative generation expansion plan, which is usually contemplated in regulations for the power system planning in most Latin American countries, modified versions of the well-known Garver's system and the IEEE-118 bus multi-area system are used to evaluate the performance of each algorithm for solving the dynamic CTEP with a medium-term planning horizon of 10 years. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with a pair of second-order mixed symmetric dual programs involving nondifferentiable functions. Weak, strong, and converse duality theorems are proved for afore-mentioned pair using the notion of second-order F-convexity/pseudoconvexity assumptions. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for the expected cost-to-go functions modeling used in the stochastic dynamic programming (SDP) algorithm. The SDP technique is applied to the longterm operation planning of electrical power systems. Using state space discretization, the Convex Hull algorithm is used for constructing a series of hyperplanes that composes a convex set. These planes represent a piecewise linear approximation for the expected cost-to-go functions. The mean operational costs for using the proposed methodology were compared with those from the deterministic dual dynamic problem in a case study, considering a single inflow scenario. This sensitivity analysis shows the convergence of both methods and is used to determine the minimum discretization level. Additionally, the applicability of the proposed methodology for two hydroplants in a cascade is demonstrated. With proper adaptations, this work can be extended to a complete hydrothermal system. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid method for modeling and solving supply chain optimization problems with soft, hard, and logical constraints. Ability to implement soft and logical constraints is a very important functionality for supply chain optimization models. Such constraints are particularly useful for modeling problems resulting from commercial agreements, contracts, competition, technology, safety, and environmental conditions. Two programming and solving environments, mathematical programming (MP) and constraint logic programming (CLP), were combined in the hybrid method. This integration, hybridization, and the adequate multidimensional transformation of the problem (as a presolving method) helped to substantially reduce the search space of combinatorial models for supply chain optimization problems. The operation research MP and declarative CLP, where constraints are modeled in different ways and different solving procedures are implemented, were linked together to use the strengths of both. This approach is particularly important for the decision and combinatorial optimization models with the objective function and constraints, there are many decision variables, and these are summed (common in manufacturing, supply chain management, project management, and logistic problems). The ECLiPSe system with Eplex library was proposed to implement a hybrid method. Additionally, the proposed hybrid transformed model is compared with the MILP-Mixed Integer Linear Programming model on the same data instances. For illustrative models, its use allowed finding optimal solutions eight to one hundred times faster and reducing the size of the combinatorial problem to a significant extent. [ABSTRACT FROM AUTHOR]

Fusing classifiers’ decisions can improve the performance of a pattern recognition system. Many applications areas have adopted the methods of multiple classifier fusion to increase the classification accuracy in the recognition process. From fully considering the classifier performance differences and the training sample information, a multiple classifier fusion algorithm using weighted decision templates is proposed in this paper. The algorithm uses a statistical vector to measure the classifier’s performance and makes a weighed transform on each classifier according to the reliability of its output. To make a decision, the information in the training samples around an input sample is used by the k-nearest-neighbor rule if the algorithm evaluates the sample as being highly likely to be misclassified. An experimental comparison was performed on 15 data sets from the KDD’99, UCI, and ELENA databases. The experimental results indicate that the algorithm can achieve better classification performance. Next, the algorithm was applied to cataract grading in the cataract ultrasonic phacoemulsification operation. The application result indicates that the proposed algorithm is effective and can meet the practical requirements of the operation. [ABSTRACT FROM AUTHOR]

This paper presents a new global optimization algorithm for solving a class of linear multiplicative programming (LMP) problem. First, a new linear relaxation technique is proposed. Then, to improve the convergence speed of our algorithm, two pruning techniques are presented. Finally, a branch and bound algorithm is developed for solving the LMP problem. The convergence of this algorithm is proved, and some experiments are reported to illustrate the feasibility and efficiency of this algorithm. [ABSTRACT FROM AUTHOR]

With an ever‐increasing number of plug‐in electric vehicles (PEVs), there is a fast‐growing interest in PEVs' charging impact on the stability and the operating cost of power grid as well as the ecological environment. The centralized coordinated charging method is one of the promising solutions to mitigate such undesired impacts as elevating load peaks, increasing energy losses, and decreasing node voltage. However, the computational complexity is a critical issue to obtain the coordinated charging strategies especially for a large number of PEVs. In this context, it is very essential to analyze the computational performance of the centralized coordinated charging methods. In this paper, a paradigm for analyzing the computational performance is provided. Three centralized methods with different standpoint, viz., to minimize carbon emissions, to minimize load variance, and to minimize generation cost, are investigated to conduct a computational performance analysis from the grid operator perspective. First, the optimization theory is employed to transform the three engineering problems into the mathematical programming models. Then, whether the mathematical programming models are convex or nonconvex is analyzed. The results show that the first two mathematical programming models are convex, and the third mathematical programming model is nonconvex. And it demonstrates that the centralized scheduling model that is convex programming has a better computational performance theoretically. At last, simulations are carried out to verify the theoretical computational performance for different types of centralized coordinated charging methods. [ABSTRACT FROM AUTHOR]

Feature scaling has attracted considerable attention during the past several decades because of its important role in feature selection. In this paper, a novel algorithm for learning scaling factors of features is proposed. It first assigns a nonnegative scaling factor to each feature of data and then adopts a generalized performance measure to learn the optimal scaling factors. It is of interest to note that the proposed model can be transformed into a convex optimization problem: second-order cone programming (SOCP). Thus the scaling factors of features in our method are globally optimal in some sense. Several experiments on simulated data, UCI data sets, and the gene data set are conducted to demonstrate that the proposed method is more effective than previous methods. [ABSTRACT FROM AUTHOR]

Safety verification determines whether any trajectory starting from admissible initial states would intersect with a set of unsafe states. In this paper, we propose a numerical method for verifying safety of a network of interconnected hybrid dynamical systems with a state constraint based on bilinear sum-of-squares programming. The safety verification is conducted by the construction of a function of states called barrier certificate. We consider a finite number of interconnected hybrid systems satisfying the input-to-state property and the networked interconnections satisfying a dissipativity property. Through constructing a barrier certificate for each subsystem and imposing dissipation-inequality-like constraints on the interconnections, safety verification is formulated as a bilinear sum-of-squares feasibility problem. As a result, safety of the interconnected hybrid systems could be determined by solving an optimization problem, rather than solving differential equations. The proposed method makes it possible to verify the safety of interconnected hybrid systems, which is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

The role of initial credit distribution scheme (ICDS) in managing network mobility has long been overlooked in previous studies of tradable credit scheme (TCS), which may make their results disputable in the reality, as the travelers possessing leftover credits can get some subsidy from the credit market and offset part of travel cost. In this paper, the disequilibrium phenomenon of previous user equilibrium (UE) solution is shown when traveler’s cognitive illusion (CI) is considered. Then, a new UE condition with TCS is defined with the ICDS and CI explicitly considered. To comprehensively reveal the impacts of ICDS on UE solution, four different types of ICDS are introduced and analyzed in a unified variational inequality (VI) modeling framework. The uniqueness of the UE link flow and market equilibrium (ME) credit price is also investigated. Furthermore, the mathematical program with equilibrium constraint (MPEC) for the optimal ICDS design problem is established, with the optimization objective being maximizing network reserve capacity. A modified relaxation algorithm is adopted to solve the MPEC. The numerical example shows that a properly designed ICDS can not only improve the network reserve capacity, but also decrease the travel cost of all the travelers in the network simultaneously. [ABSTRACT FROM AUTHOR]

A day-ahead dispatch strategy for the integrated system of wind/photovoltaic/pumped-storage/gas-turbine-power/energy storage is proposed based on the multi-frequency scale power of wind/photovoltaic (PWP). First, filter analysis of the PWP is carried out according to the control target of the system to get the components of PWP under different frequency scales; thus, the power output of different compensatory plants can be scheduled. Second, an improved particle swarm optimization algorithm is utilized to parallel optimize costs of different plants and calculate the overall power output of the integrated system. Finally, based on different dispatch modes, considering system stability and the penetration ability of wind/photovoltaic, the per-unit generation cost of the integrated system is optimized and the power output is scheduled. Simulation results show that, compared with traditional optimization models and algorithms, the proposed strategy is capable of smoothing the power fluctuation caused by large-scale wind/photovoltaic integration, as well as realizing economical, efficient and environmentally friendly operation of the system. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the analysis and design of positivity and stability of linear continuous conic systems. First, two robustness analysis theorems are proposed for the systems with state-feedback. Second, the state-feedback stabilization problem is solved by using linear programming (LP). Numerical examples are given for illustration. Finally, the conclusions are made. [ABSTRACT FROM AUTHOR]

In freight transportation there are two main distribution strategies: direct shipping and multiechelon distribution. In the direct shipping, vehicles, starting from a depot, bring their freight directly to the destination, while in the multiechelon systems, freight is delivered from the depot to the customers through an intermediate points. Multiechelon systems are particularly useful for logistic issues in a competitive environment. The paper presents a concept and application of a hybrid approach to modeling and optimization of the Multi-Echelon Capacitated Vehicle Routing Problem. Two ways of mathematical programming (MP) and constraint logic programming (CLP) are integrated in one environment. The strengths of MP and CLP in which constraints are treated in a different way and different methods are implemented and combined to use the strengths of both. The proposed approach is particularly important for the discrete decision models with an objective function and many discrete decision variables added up in multiple constraints. An implementation of hybrid approach in the ECLiPSe system using Eplex library is presented. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) and its variants are shown as an illustrative example of the hybrid approach. The presented hybrid approach will be compared with classical mathematical programming on the same benchmark data sets. [ABSTRACT FROM AUTHOR]

This paper proposes an improved geometric programming approach to address the optimization of biochemical systems. In the proposed method we take advantage of a special and interesting class of nonlinear kinetic models known as generalized mass action (GMA) models. In most situations optimization problems with GMA models are nonconvex and difficult problems to solve for global optimality. To deal with this difficulty, in this work, some transformation strategy is first used to convert the optimization problem with GMA models into an equivalent problem. Then a convexification technique is applied to transform this resulting optimization problem into a series of standard geometric programming problems that can be solved to reach a global solution. Two case studies are presented to demonstrate the advantages of the proposed method in terms of computational efficiency. [ABSTRACT FROM AUTHOR]

Bioinspired optimization algorithms have been widely used to solve various scientific and engineering problems. Inspired by biological lifecycle, this paper presents a novel optimization algorithm called lifecycle-based swarm optimization (LSO). Biological lifecycle includes four stages: birth, growth, reproduction, and death. With this process, even though individual organism died, the species will not perish. Furthermore, species will have stronger ability of adaptation to the environment and achieve perfect evolution. LSO simulates Biological lifecycle process through six optimization operators: chemotactic, assimilation, transposition, crossover, selection, and mutation. In addition, the spatial distribution of initialization population meets clumped distribution. Experiments were conducted on unconstrained benchmark optimization problems and mechanical design optimization problems. Unconstrained benchmark problems include both unimodal and multimodal cases the demonstration of the optimal performance and stability, and the mechanical design problem was tested for algorithm practicability. The results demonstrate remarkable performance of the LSO algorithm on all chosen benchmark functions when compared to several successful optimization techniques. [ABSTRACT FROM AUTHOR]

Electric power is an important energy in steel industry. Electricity accounts for roughly 20%to 30% of the gross energy consumption and costs about 10% of the gross cost of energy. In this paper, under the premise of ensuring the stability of energy supply and the normal production safety, the mathematical programming method and the dynamic mathematical optimization model were used to set up the surplus gas in the optimal allocation among the buffer users and steam production dispatching for the production equipment. The application of this optimization model can effectively improve the energy efficiency and the accuracy of power generation, making full use of secondary energy and residual heat. It also can realize the rationalization of the electricity production structure optimization which can effectively reduce the flare of the gas and steam on one hand, and save energy and decrease production cost on the other. [ABSTRACT FROM AUTHOR]

This paper presents a novel optimization method for effectively solving nonconvex quadratically constrained quadratic programs (NQCQP) problem. By applying a novel parametric linearizing approach, the initial NQCQP problem and its subproblems can be transformed into a sequence of parametric linear programs relaxation problems. To enhance the computational efficiency of the presented algorithm, a cutting down approach is combined in the branch and bound algorithm. By computing a series of parametric linear programs problems, the presented algorithm converges to the global optimum point of the NQCQP problem. At last, numerical experiments demonstrate the performance and computational superiority of the presented algorithm. [ABSTRACT FROM AUTHOR]

With the increasing reliance on modeling optimization problems in practical applications, a number of theoretical and algorithmic contributions of optimization have been proposed. The approaches developed for treating optimization problems can be classified into deterministic and heuristic. This paper aims to introduce recent advances in deterministic methods for solving signomial programming problems and mixed-integer nonlinear programming problems. A number of important applications in engineering and management are also reviewed to reveal the usefulness of the optimization methods. [ABSTRACT FROM AUTHOR]

This paper proposes a union of hyperspheres by the mixed-integer nonlinear program to classify biological and medical datasets. A classifying program with nonlinear terms uses piecewise linearization technique to obtain a global optimum. The numerical examples illustrate that the proposed method can obtain the global optimum more effectively than current methods. [ABSTRACT FROM AUTHOR]

The mode-to-mode transition problem involves taking initial states in the start mode to the equilibrium point of the goal mode, where each mode of operation corresponds to an operating regime about an equilibrium point. Like the problem of dynamic transitions between various equilibria, there is no consistent theory that deals with the mode-to-mode transition problem. This paper presents a method of designing mode-to-mode controllers by blending the start and goal mode controllers. The blending gains are determined by the phase portrait assignment algorithm. The phase portrait assignment algorithm is a systematic technique that uses dynamic programming and center-point cell mapping to design fuzzy logic controllers. A hover mode to forward flight mode controller for a small-scale helicopter is synthesized to illustrate the design methodology. Simulation results show that the controller is able to transition stably from hover to forward flight. Finally, sensitivity analysis of the hover to forward flight controller is performed for small parameter perturbations. © 2000 John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

In this study, we developed a model which elaborates relationship among efficiency of an estimator and survey cost. This model is based on a multiobjective optimization programming structure. Survey cost and efficiency of related estimator(s) lie in different directions, i.e., if one increases, the other decreases. The model presented in this study computes cost for a desired level of efficiency on various characteristics (goals). The calibrated model minimizes the cost for the compromise optimal sample selection from different strata when characteristic j is subject to achieve at least 1−αj level of efficiency of its estimator. In the first step, the proposed model minimizes the variance for a fixed cost, and it then finds the rise in cost for an αj percent rise in efficiency of any characteristic j. The resultant model is a multiobjective compromise allocation goal programming model. [ABSTRACT FROM AUTHOR]

BACKGROUND: Bone diseases caused by an imbalance of bone turnover represent a major public health concern worldwide. Studies involving bone remodelling mechanisms can assist in the treatment of osteoporosis, osteopenia and in cases of fractures. In recent decades several authors have developed bone remodelling models. AIM: The aim of this study is to propose a model based on the thermodynamic framework to describe the process of bone remodelling. A secondary aim is to model a trabecula subjected to cyclic loading and calibrate the model with experimental data. METHODS: Thermodynamic potentials are used to generate the functions of state based on internal scalar variables. The evolution of the variables in time is determined by dissipation potentials, which are created through the use of convex analysis. Constitutive equations are solved with mathematical programming algorithms and the numerical implementation of this theory uses the Finite Elements Method for spatial discretization. RESULTS: The proposed theory was applied to a one-dimensional example, and two situations (an undamaged material and an initially damaged material) were simulated. The one-dimensional example shows a microscopic view of a trabecula under the influence of a growing load cycle throughout 1200 days. This dynamic process may represent the rehabilitation of an athlete, starting with light exercises up to a very heavy physical activity. CONCLUSIONS: The model was able to represent one bone remodelling cycle in the trabecula. Although it is not yet possible to obtain an experimental curve of a traction test in vivo, the in silico model showed a process of damage that is similar to the static test of the literature. The results also suggest a modification in the equation adopted for the Helmholtz potential shown here. This study presents a consistent thermodynamic formalism for bone remodelling, which may allow further contributions as the incorporation of chemical reactions, mass transference and anisotropic damage. [ABSTRACT FROM AUTHOR]

Fixed-basis and variable-basis approximation schemes are compared for the problems of function approximation and functional optimization (also known as infinite programming). Classes of problems are investigated for which variable-basis schemes with sigmoidal computational units perform better than fixed-basis ones, in terms of the minimum number of computational units needed to achieve a desired error in function approximation or approximate optimization. Previously known bounds on the accuracy are extended, with better rates, to families of d-variable functions whose actual dependence is on a subset of d' ≪ d variables, where the indices of these d' variables are not known a priori. [ABSTRACT FROM AUTHOR]

A class of G-semipreinvex functions, which are some generalizations of the semipreinvex functions, and the G-convex functions, is introduced. Examples are given to show their relations among G-semipreinvex functions, semipreinvex functions and G-convex functions. Some characterizations of G-semipreinvex functions are also obtained, and some optimality results are given for a class of G-semipreinvex functions. Ours results improve and generalize some known results. [ABSTRACT FROM AUTHOR]

This work deals with numerical methods of parameter optimization for asymptotically stable systems. We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system. [ABSTRACT FROM AUTHOR]

A sensitivity analysis and multicriteria control optimization formulation is derived for mechanical systems. This formulation is implemented into an interactive optimum design code and it is applied to optimize protection systems for the prevention of injuries. The limiting isolation capabilities of the systems are determined. The effect of pre-acting control is investigated. Control forces as well as the time at which the control should act before the instant of impact are considered as design variables. The same idea used by the authors in previous articles for minimum time control problems is applied here to find the preview time. Dynamic response index, maximum acceleration, rattlespace, or maximum power of the resisting force among others can be used as performance criteria. In order to handle the multicriteria problem, both the reduced feasible region method and a min-max upper bound method are utilized. The adjoint system approach is used to calculate the sensitivities. The dynamic response of the systems and its sensitivity are discretized via space-time finite elements. The equations of motion and the sensitivity equations are integrated at-once as it is typical for the static response. This way, displacement, velocity or acceleration control conditions can be imposed easily at any point in time. Also, adjoint system response is obtained without needing primary response memorization. Mathematical programming is used for the optimal control process. [ABSTRACT FROM AUTHOR]