Directional derivatives of value functions play an essential role in the sensitivity and stability analysis of parametric optimization problems, in studying bi-level and min-max problems, in quasi-differentiable calcu...
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Directional derivatives of value functions play an essential role in the sensitivity and stability analysis of parametric optimization problems, in studying bi-level and min-max problems, in quasi-differentiable calculus. Their calculation is studied in numerous works by A.V. Fiacco, V.F. Demyanov and A.M. Rubinov, R.T. Rockafellar, A. Shapiro, J.F. Bonnans, A.D. Ioffe, A. Auslender and R. Cominetti, and many other authors. This article is devoted to the existence of the second order directional derivatives of value functions in parametric problems with non-single-valued solutions. The main idea of the investigation approach is based on the development of the method of the first-order approximations by V.F. Demyanov and A.M. Rubinov.
We consider the problem of choosing the levels of a set of advertising media in order to maximize the firm profit when the market is heterogeneous. Advertising efforts affect the demand of the different segments varia...
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We consider the problem of choosing the levels of a set of advertising media in order to maximize the firm profit when the market is heterogeneous. Advertising efforts affect the demand of the different segments variably and we assume that the advertising effects on demand over time are mediated by a vector goodwill variable. A first general advertising decision problem is stated and solved in the non-linear programming framework. A preference index is then obtained for the medium selection problem when each segment demand function is linear in goodwill and each medium advertising cost function is quadratic in its level. Finally the theoretical case of disjoint advertising media is discussed.
Scalarization in vector optimization is often closely connected to the minimization of Gerstewitz functionals. In this paper, the minimizer sets of Gerstewitz functionals are investigated. Conditions are given under w...
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Scalarization in vector optimization is often closely connected to the minimization of Gerstewitz functionals. In this paper, the minimizer sets of Gerstewitz functionals are investigated. Conditions are given under which such a set is nonempty and compact. Interdependencies between solutions of problems with different parameters or with different feasible point sets are shown. Consequences for the parameter control in scalarization methods are proved. It is pointed out that the minimization of Gerstewitz functionals is equivalent to an optimization problem which generalizes the scalarization by Pascoletti and Serafini. The results contain statements about minimizers of certain Minkowski functionals and norms. Some existence results for solutions of vector optimization problems are derived.
The main aim of this paper is to develop an approach to solving multi-objective bi-matrix games with intuitionistic fuzzy (IF) goals, which are called IF multi-objective bi-matrix games for short. In this paper, the s...
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The main aim of this paper is to develop an approach to solving multi-objective bi-matrix games with intuitionistic fuzzy (IF) goals, which are called IF multi-objective bi-matrix games for short. In this paper, the solution approach for such a game is presented by introducing an aspiration level approach, and IF non-linear programming problem is constructed to find the optimal solution for such types of multi-objective bi-matrix games. Furthermore, it is shown that this multi-objective bi-matrix game with IF goals is an extension of the multi-objective bi-matrix game with fuzzy goals. Finally, a numerical example is incorporated to demonstrate the implementation and applicability process of the proposed approach.
The problem of determining economic production quantities and demands, with respect to prices for a hybrid manufacturing / remanufacturing system is addressed in this paper. Most of studies in the literature consider ...
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The problem of determining economic production quantities and demands, with respect to prices for a hybrid manufacturing / remanufacturing system is addressed in this paper. Most of studies in the literature consider same market for new and remanufactured (as-good-as new assumption) and separate production line. We consider in this paper that products are processed on a common line and are sold in distinct market with price sensitive demands. The problem is modelled and solved with a non-linear model. A numerical analysis is developed to validate the model and analyze its feasibility and limits.
We consider convex Semi-Infinite programming (SIP) problems with a continuum of constraints. For these problems we introduce new concepts of immobility orders and immobile indices. These concepts are objective and imp...
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We consider convex Semi-Infinite programming (SIP) problems with a continuum of constraints. For these problems we introduce new concepts of immobility orders and immobile indices. These concepts are objective and important characteristics of the feasible sets of the convex SIP problems since they make it possible to formulate optimality conditions for these problems in terms of optimality conditions for some NLP problems (with a finite number of constraints). In the paper we describe a finite algorithm (DIO algorithm) of determination of immobile indices together with their immobility orders, study some important properties of this algorithm, and formulate the Implicit Optimality Criterion for convex SIP without any constraint qualification conditions (CQC). An example illustrating the application of the DIO algorithm is provided.
The particle swarm optimization (PSO) algorithm has been recently introduced in the non-linear programming, becoming widely studied and used in a variety of applications. Starting from its original formulation, many v...
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The particle swarm optimization (PSO) algorithm has been recently introduced in the non-linear programming, becoming widely studied and used in a variety of applications. Starting from its original formulation, many variants for improvement and specialization of the PSO have been already proposed, but without any definitive result, thus research in this area is nowadays still rather active. This paper goes in this direction, by proposing some modifications to the basic PSO algorithm, aiming at enhancements in aspects that impact the efficiency and accuracy of the optimization algorithm. In particular, variants of PSO based on fuzzy logics and Bayesian theory have been developed, which show better, or competitive, performances compared to both the basic PSO formulation and a few other optimization algorithms taken from the literature.
This paper proposes the software package SISCON, dedicated to the evaluation of optimal decisions for large scale systems. SISCON firstly evaluates mathematical models developed from experimental data using LS methods...
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This paper proposes the software package SISCON, dedicated to the evaluation of optimal decisions for large scale systems. SISCON firstly evaluates mathematical models developed from experimental data using LS methods for linear and nonlinear systems and after that computes the optimal decision problems, solving the mathematical non-linear programming problems. The large scale systems have generally a complex structure and global approach computation cannot be carried out. The authors present a decentralised decision structure having a well-defined distribution of supervisory functions. After decomposition of large – scale problems is carried out, sub problems are solved using standard optimization techniques. SISCON offers opportunities for solving non-linear mathematical programming problems and for evaluating optimal decisions in large scale systems control.
State estimation for a class of non-linear, continuous-time dynamic systems affected by disturbances is investigated. The estimator is assigned a given structure that depends on an innovation function taking on the fo...
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State estimation for a class of non-linear, continuous-time dynamic systems affected by disturbances is investigated. The estimator is assigned a given structure that depends on an innovation function taking on the form of a ridge computational model, with some parameters to be optimized. The behaviour of the estimation error is analysed by using input-to-state stability. The design of the estimator is reduced to the determination of the parameters in such a way as to guarantee the regional exponential stability of the estimation error in a disturbance-free setting and to minimize a cost function that measures the effectiveness of the estimation when the system is affected by disturbances. Stability is achieved by constraining the derivative of a Lyapunov function to be negative definite on a grid of points, via the penalization of the constraints that are not satisfied. Low-discrepancy sampling techniques, typical of quasi-Monte Carlo methods, are exploited in order to reduce the computational burden in finding the optimal parameters of the innovation function. Simulation results are presented to investigate the performance of the estimator in comparison with the extended Kalman filter and in dependence of the complexity of the computational model and the sampling coarseness.
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