Input optimization: I. Optimal realizations of mathematical models

Zlobec, Sanjo

doi:10.1007/bf02591948

Cited by 19 publications

(19 citation statements)

References 17 publications

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“…(Different initial 0 ° generally result in different optimal inputs 0", even in linear models.) The level of optimization, dealing with such continuous optimization of mathematical models is termed 'input optimization', see [85][86][87][88][89] (abbreviation: IO). In IO the model (P, 0) is considered to be a 'black box', the parameter 0 is the 'input' and the triple {F(0),/~(0),f(0)} is the 'output'.…”

Section: Input Optimizationmentioning

confidence: 99%

“…A major obstacle is that this function is not represented analytically, so the efficient numerical methods of nonsmooth optimization (see [51,95]) are not directly applicable. Moreover, f(0) is generally neither convex nor concave, even for linear models (see [50,85]), so the usual convexity arguments do not apply.…”

Section: Nonsmooth Analysis and Input Optimizationmentioning

confidence: 99%

“…In Section 6 we assume that the model functions are differentiable. Since the regions of stability are conditions that guarantee local (and often global) continuity of the feasible set mapping (for all "reasonable" objective functions), we can extend the results from single-objective to multi-objective models in a rather straightforward way using properly efficient Pareto solutions [29,39,56,84,87]. This is the subject of Section 7.…”

Section: Outlinementioning

confidence: 99%

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Characterizing optimality in mathematical programming models

Zlobec

1988

Acta Appl Math

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This paper is a survey of basic results that characterize optimality in single-and multiobjective mathematical programming models. Many people believe, or want to believe, that the underlying behavioural structure of management, economic, and many other systems, generates basically 'continuous' processes. This belief motivates our definition and study of optimality, termed 'structural' optimality. Roughly speaking, we say that a feasible point of a mathematical programming model is structurally optimal if every improvement of the optimal value function, with respect to parameters, results in discontinuity of the. corresponding feasible set of decision variables. This definition appears to be more suitable for many applications and it is also more general than the usual one: every optimum is a structural optimum but not necessarily vice versa. By characterizing structural optima, we obtain some new, and recover the familiar, optimality conditions in nonlinear programming.The paper is self-contained. Our approach is geometric and inductive: we develop intiution by studying finite-dimensional models before moving on to abstract situations.AMS subject clmsilieatiom (1980). 90C25, 90C48, 90C31, 54C10. 54C60, 49B27, 49B50.

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Section: Input Optimizationmentioning

confidence: 99%

Section: Nonsmooth Analysis and Input Optimizationmentioning

confidence: 99%

Section: Outlinementioning

confidence: 99%

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Characterizing optimality in mathematical programming models

Zlobec

1988

Acta Appl Math

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“…in global optimization or to provide means of improving the optimal solutions of specific systems by proposing variations to the parameters of the model [Guddat et al, 1990 andZlobec, 1985].…”

Section: Industry Implementationsmentioning

confidence: 99%

A general parametric optimal power flow

Almeida

Galiana

Soares

1994

IEEE Trans. Power Syst.

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“…This problem was investigated in [1] as a parameterized version of the MTSP, which was defined in [2], with penalized earliness in starting and lateness in the completion of the operation. The authors in [1] applied the optimal choice concept which is given in [3] and some theoretical results from [4] to obtain the optimal values of the given parameters.…”

Section: Introductionmentioning

confidence: 99%

The Solution of Machines’ Time Scheduling Problem Using Artificial Intelligence Approaches

Ghoniemy¹,

El‐Sawy²,

Shohla³

et al. 2012

IJARAI

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Abstract-The solution of the Machines' Time Scheduling Problem (MTSP) is a hot point of research thatis not yet matured, and needs further work. This paper presents two algorithms for the solution of the Machines' Time Scheduling Problem that leads to the best starting time for each machine in each cycle. The first algorithm is genetic-based (GA) (with nonuniform mutation), and the second one is based on particle swarm optimization (PSO) (with constriction factor). A comparative analysis between both algorithms is carried out. It was found that particle swarm optimization gives better penalty cost than GA algorithm and max-separable technique, regarding best starting time for each machine in each cycle.

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Input optimization: I. Optimal realizations of mathematical models

Cited by 19 publications

References 17 publications

Characterizing optimality in mathematical programming models

Characterizing optimality in mathematical programming models

A general parametric optimal power flow

The Solution of Machines’ Time Scheduling Problem Using Artificial Intelligence Approaches

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