Showing papers in "Journal of Optimization Theory and Applications in 1983"
TL;DR: A new version, known as CRS2, of the author's controlled random search procedure for global optimization (CRS), is described, which is simpler and requires less computer storage than the original version, yet it has a comparable performance.
Abstract: The paper describes a new version, known as CRS2, of the author's controlled random search procedure for global optimization (CRS). The new procedure is simpler and requires less computer storage than the original version, yet it has a comparable performance. The results of comparative trials of the two procedures, using a set of standard test problems, are given. These test problems are examples of unconstrained optimization. The controlled random search procedure can also be effective in the presence of constraints. The technique of constrained optimization using CRS is illustrated by means of examples taken from the field of electrical engineering.
351 citations
TL;DR: In this paper, a new time-domain-based approach is developed for the perturbation analysis of queueing networks, which can derive sensitivity information of the throughput of the system with respect to various parameters.
Abstract: A new time-domain-based approach is developed in this paper for the perturbation analysis of queueing networks. We show that, by observing a single sample path realization of the network trajectory, we can derive sensitivity information of the throughput of the system with respect to various parameters. This information can then be used for the optimization of queueing networks. Numerous experiments as well as analytical results demonstrating the validity of this new approach are given and discussed.
285 citations
TL;DR: In this paper, the problem of observation spillover in self-adjoint distributed-parameter systems is investigated, and two techniques of state estimation (i.e., observers and modal filters) are described.
Abstract: The problem of observation spillover in self-adjoint distributed-parameter systems is investigated. Observation spillover occurs when the output of a limited number of sensors, located at various points on the distributed domain, cannot synthesize the modal coordinates exactly. To this end, two techniques of state estimation (namely, observers and modal filters) are described. Both techniques can be used to extract modal coordinates from the system output and to implement feedback controls. It is shown that, if the residual modes are included in the observer dynamics, observation spillover cannot lead to instability in the residual modes. The problem of the unmodeled modes does remain, however. It is also shown that the modal filters have some very attractive features. In particular, modal filters can be designed to estimate the modal coordinates with such accuracy that observation spillover can be virtually eliminated. In addition, when modal filters are used, in conjunction with a sufficiently large number of sensors, the entire infinity of the system modes can be regarded as modeled, which implies that actual distributed control of the system is possible. It is also demonstrated that modal filters are quite easy to design and are not plagued by instability problems.
183 citations
TL;DR: In this article, a class of adaptive controllers for dynamical systems containing uncertain elements due to imperfect knowledge about the model and the input is presented. But these controllers are not suitable for dynamic systems with a large number of unknown elements.
Abstract: We consider dynamical systems containing uncertain elements due to imperfect knowledge about the model and the input. Since these uncertainties may result in unstable behavior, we seek controllers which guarantee that all possible responses of the system are uniformly bounded and approach a desired response. Toward that end, we present a class of adaptive controllers.
171 citations
TL;DR: An analytical expression for the volume of the convex polyhedron {x¦Ax⩽b} is given in this paper, based on a simple recursive identity, it yields an efficient algorithm.
Abstract: An analytical expression for the volume of the convex polyhedron {x¦Ax⩽b} is given. Based on a simple recursive identity, it yields an efficient algorithm. Redundant constraints can be detected.
140 citations
TL;DR: In this article, the shifted Legendre polynomial series is employed to solve variational problems and the solution is carried out by using an operational matrix for integrating the shift Legendre vector.
Abstract: The shifted Legendre polynomial series is employed to solve variational problems. The solution is carried out by using an operational matrix for integrating the shifted Legendre polynomial vector. Variational problems are reduced to solving algebraic equations. Two illustrative examples are given, and the computational results obtained by Legendre series direct method are compared with the exact solutions.
129 citations
TL;DR: In this article, the sets of Pareto-optimal and weakly paretooptimal solutions to a vector maximization problem defined by a continuous vector-valued quasiconcave criterion function and a closed convex set of alternatives are studied.
Abstract: We study the sets of Pareto-optimal and weakly Pareto-optimal solutions to a vector maximization problem defined by a continuous vector-valued quasiconcave criterion functionf and a closed convex set of alternativesS. IfS is compact, it is shown that the set of weakly Pareto-optimal alternatives is connected, but that the set of Pareto-optimal alternatives is not necessarily connected. However, the set of Pareto optima is shown to be connected for some important subclasses of quasiconcave functions. We also provide some reasonable conditions under which the compactness assumption onS may be relaxed and connectedness maintained.
119 citations
TL;DR: In this article, an operational matrix for the integration of Laguerre polynomials is introduced, and the variational problems are reduced to the solution of algebraic equations, and an illustrative example is given.
Abstract: A direct method for solving variational problems via Laguerre series is presented. First, an operational matrix for the integration of Laguerre polynomials is introduced. The variational problems are reduced to the solution of algebraic equations. An illustrative example is given.
112 citations
TL;DR: This paper formally establishes connections between two standard approaches proposed for resolving multi-objective programs, namely, the nonpreemptive and the preemptive methods, and demonstrates in the linear case that there exists a set of weights, such that any optimal solution to the nonPreemptive problem is optimal to the preemptives problem.
Abstract: In this paper, we formally establish connections between two standard approaches proposed for resolving multi-objective programs, namely, the nonpreemptive and the preemptive methods. We demonstrate in the linear case that, if the preemptive problem has an optimal solution, then there exists a set of weights for the nonpreemptive problem, such that any optimal solution to the nonpreemptive problem is optimal to the preemptive problem. Conversely, and more importantly, any optimal solution to the preemptive problem is optimal to the nonpreemptive problem. A similar result is established for arbitrary multi-objective functions being optimized over a finite discrete set. Thus, the preemptive problem is subsumed within the nonpreemptive problem in these cases. Although we actually construct a set of equivalent weights, we do not advocate our technique as a computational device for solving the preemptive problem. However, a previous attempt (Ref. 1), which does prescribe a set of equivalent weights to solve a preemptive problem as a linear program, is shown to be erroneous. Moreover, our constructive proof exhibits the features of the problem which govern the determination of such equivalent weights.
99 citations
TL;DR: In this paper, it was shown that duality can be obtained for non-convex generalized fractional programs using only a basic result on linear inequalities, in both the linear case and the nonlinear case.
Abstract: For fractional programs involving several ratios in the objective function, a dual is introduced with the help of Farkas' lemma. Often the dual is again a generalized fractional program. Duality relations are established under weak assumptions. This is done in both the linear case and the nonlinear case. We show that duality can be obtained for these nonconvex programs using only a basic result on linear (convex) inequalities.
82 citations
TL;DR: In this paper, the necessary conditions of Fritz John and Kuhn-Tucker type for Pareto optimality are derived by first reducing a vector minimization problem (multiobjective programming) to a system of scalar minimization problems and then using known results in convex programming.
Abstract: Necessary conditions of Fritz John and Kuhn-Tucker type for Pareto optimality are derived by first reducing a vector minimization problem (multiobjective programming) to a system of scalar minimization problems and then using known results in convex programming.
TL;DR: In this article, the authors generalize the well-known notions of minimax, maximin, and saddle point to vector-valued functions and give conditions for a vectorvalued function to have a generalized saddle point.
Abstract: In this paper, we generalize the well-known notions of minimax, maximin, and saddle point to vector-valued functions. Conditions for a vector-valued function to have a generalized saddle point are given. An example is used to illustrate the generalized concepts of minimax, maximin, and saddle point.
TL;DR: In this article, the non-differentiable optimization theory with equality and inequality constraints is extended to a multiobjective program on a Banach space, and generalized conditions of the Fritz-John type given by Clarke's generalized gradient formula are derived for weak Pareto-optimal solutions.
Abstract: The nondifferentiable optimization theory with equality and inequality constraints is extended to a multiobjective program on a Banach space. We derive generalized conditions of the Fritz-John type given by Clarke's generalized gradient formula, which are necessary for weak Pareto-optimal solutions.
TL;DR: In this article, the authors derived an error estimate which enables them to determine an upper bound for the size of the sequence of modified Newton iterates, assuming that the Kantorovich hypotheses are satisfied.
Abstract: The solution of nonlinear, two-point boundary value problems by Newton's method requires the formation and factorization of a Jacobian matrix at every iteration. For problems in which the cost of performing these operations is a significant part of the cost of the total calculation, it is natural to consider using the modified Newton method. In this paper, we derive an error estimate which enables us to determine an upper bound for the size of the sequence of modified Newton iterates, assuming that the Kantorovich hypotheses are satisfied. As a result, we can efficiently determine when to form a new Jacobian and when to continue the modified Newton algorithm. We apply the result to the solution of several nonlinear, two-point boundary value problems occurring in combustion.
TL;DR: In this article, a new approach to the optimization of discrete-event dynamic systems has been developed, which requires answering the following question: given an observed value of the outcome of a random variable, what would have been the outcome if the parameters of the random variable had been different?
Abstract: A new approach to the optimization of discrete-event dynamic systems has recently been developed (Refs 1---4) The implementation of this approach requires answering the following question: given an observed value of the outcome of a random variable, what would have been the outcome if the parameters of the random variable had been different? The answer to this question would traditionally involve the value of an outcome in an underlying sample space However, this underlying value cannot normally be observed In this note, we give a framework for answering this question, in terms of the observed value alone This point had not been considered rigorously in the new approach of Refs 1---4, and our note derives a basic equation required for that approach
TL;DR: In this paper, the shape design sensitivity of a typical integral functional is determined, and explicit and computable formulas for the derivative (first variation) of the structural response and the eigenvalues with respect to the shape of a membrane are presented.
Abstract: The dependence of the static response and the eigenvalues of a membrane on its shape is characterized. A transformation function is defined to determine the shape of the membrane. Differential operator properties and transformation techniques of integral calculus are employed to show that the static response and the eigenvalues of the system depend in a continuous and differentiable way on the shape of the membrane. Explicit and computable formulas are presented for the derivative (first variation) of the structural response and the eigenvalues with respect to the shape. A rigorous proof is provided, and the shape design sensitivity of a typical integral functional is determined.
TL;DR: In this paper, the authors derived sufficient conditions for controllability and necessary conditions for minimum in nonsmooth optimal control problems defined by differential or functional-integral equations with isoperimetric and unilateral restrictions.
Abstract: We derive sufficient conditions for controllability and necessary conditions for minimum in nonsmooth optimal control problems defined by differential or functional-integral equations with isoperimetric and unilateral restrictions. We consider the cases when the controls are relaxed or chosen fromabundant sets of original (ordinary) controls (which include most, or all, of the control sets studied in the literature). We prove that, if there exist optimal strictly original controls (that is, controls that are optimal in an abundant set but not among relaxed controls), then the problem admits abnormal extremals. We also study the abnormality of the optimal strictly original controls themselves.
TL;DR: In this article, the authors treat multiple-objective problems in which solutions are sought which are maximal (efficient, nondominated) under an order which may be nonconical.
Abstract: Previous theoretical work in multiple-objective optimization has focused entirely on vector orders representable by positive cones. Here, we treat multiple-objective problems in which solutions are sought which are maximal (efficient, nondominated) under an order which may be nonconical. Compactness conditions under which maximal solutions exist and bound the remaining alternatives are given. First-order necessary conditions and first-order sufficient conditions for maximality in general normed linear spaces are derived, and a scalarization result is given. A small computational example is also presented. Several previous results are special cases of those given here.
TL;DR: In this paper, an optimal control problem, which includes restrictions on the controls and equality/inequality constraints on the terminal states, is formulated, and second-order necessary conditions of the accessory-problem type are obtained in the absence of normality conditions.
Abstract: An optimal control problem, which includes restrictions on the controls and equality/inequality constraints on the terminal states, is formulated. Second-order necessary conditions of the accessory-problem type are obtained in the absence of normality conditions. It is shown that the necessary conditions generalize and simplify prior results due to Hestenes (Ref. 5) and Warga (Refs. 6 and 7).
TL;DR: In this article, the authors derived essentially nonunique closed-loop Nash equilibria for a class of nonzero-sum differential games with a unique and degenerated feedback Nash equilibrium.
Abstract: In this paper, we derive essentially nonunique closed-loop Nash equilibria for a class of nonzero-sum differential games with a unique and degenerated feedback Nash equilibrium.
TL;DR: In this paper, a solution algorithm for a single machine scheduling problem with two criteria: total tardiness and total flow time is presented, which is then incorporated into a multiple-criteria dynamic programming framework to improve the computational efficiency.
Abstract: This paper presents a solution algorithm for a single machine scheduling problem with two criteria: total tardiness and total flow time. Theoretical results of precedence properties which are respected by all nondominated schedules are first derived. These precedence properties are then incorporated into a multiple-criteria dynamic programming framework to improve the computational efficiency. Results of the computational experiment and the average behavior (computation time and efficiency) of the algorithm are reported.
TL;DR: In this article, an alternative characterization of the class of self-bounded controlled invariant subspaces was given, which was introduced by Basile and Marro in Ref. 1.
Abstract: An alternative characterization is given of the class of self-bounded controlled invariant subspaces that was introduced by Basile and Marro in Ref. 1. We also prove a result that was stated as a conjecture in the cited paper.
TL;DR: In this article, the authors considered the Cauchy problem for the heat equation with a potential term (imaginary time analogue of the Schrodinger equation) and showed that a positive solution to this problem turns into a solution to the dynamic programming equation for a problem of stochastic calculus of variations.
Abstract: The Cauchy problem for the heat equation with a potential term (imaginary time analogue of the Schrodinger equation) is considered. After a logarithmic transformation, a positive solution to this Cauchy problem turns into a solution to the dynamic programming equation for a problem of stochastic calculus of variations. The latter problem is one of least average action. The classical principle of least action is obtained as an appropriate parameter tends to zero.
TL;DR: In this paper, the stabilization problem for linear delay systems containing uncertain elements is studied and it is shown that if the matching conditions are satisfied and the uncertainties in the control matrix are not too large, there exist linear current-response feedback controls which guarantee asymptotic stability of the zero response of the system, no matter what the uncertainties and initial conditions are.
Abstract: This note concerns the stabilization problem for linear delay systems containing uncertain elements. If the so-called matching conditions are satisfied and the uncertainties in the control matrix are not too large, there exist linear current-response feedback controls which guarantee asymptotic stability of the zero response of the system, no matter what the uncertainties and initial conditions are.
TL;DR: In this article, the expected number of steps of Matya's random optimization method applied to the constrained nonlinear minimization problem is estimated. But it is shown that this random optimization can be optimized by the uniform distribution, in which case the exact value of the expected time complexity is computed.
Abstract: In this paper, we give an estimate of the expected number of steps of Matya's random optimization method applied to the constrained nonlinear minimization problem. It is also shown that, in a sense, this random optimization method can be optimized by the uniform distribution, in which case the exact value of the expected number of steps is computed.
TL;DR: In this paper, the basic properties of arcwise connected sets and functions are investigated, and it is shown that all the functions involved are not necessarily differentiable, but they are generalizations of convexity.
Abstract: The purpose of this paper is to investigate some elementary, basic properties of arcwise connected sets and functions. Since these concepts are generalizations of convexity, it is natural to ask if any of the basic properties of convex sets and functions are carried over to these new generalized classes. All the functions involved are considered to be not necessarily differentiable.
IBM1
TL;DR: In this article, the problem of scheduling personnel and jobs to minimize personnel idle time, by integer programming, is formulated and solved for a set of maintenance jobs to be processed over a fixed time horizon, where each job is divided into finite time intervals in which the skills required are known.
Abstract: Given (i) a set of maintenance jobs to be processed over a fixed time horizon, (ii) the breakdown of each job into finite time intervals in which the skills required are known, and (iii) the pool of available manpower for each skill type over the horizon, we formulate and solve the problem of scheduling personnel and jobs to minimize personnel idle time, by integer programming.
TL;DR: In this paper, the asymptotic order of accuracy of Tikhonov's method for approximating the minimal norm least-square solution of an ill-posed operator equation is investigated.
Abstract: In this paper, the asymptotic order of accuracy (with respect to the error level δ in the data) of Tikhonov's method for approximating the minimal norm least-square solution of an ill-posed operator equation is investigated. It is shown that, except for finite rank operators, the orderO(δ2/3) is best possible.
TL;DR: In this paper, a general class of scalarization methods for multiple-objective optimization is presented, and it is shown how the optimal solutions characterize the properly efficient points, and how to obtain the optimal solution.
Abstract: A general class of scalarization methods for multiple-objective optimization is presented. It is then shown how the optimal solutions characterize the properly efficient points.
IBM1
TL;DR: The problem of scheduling plant maintenance personnel has been recast to give the minimum problem-size formulation as discussed by the authors, where the problem of finding the minimum number of maintenance personnel is solved.
Abstract: The problem of scheduling plant maintenance personnel has been recast to give the minimum problem-size formulation.