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In this paper, using generalized algebraic operations introduced by Ben-Tal [7], we introduce new classes of (h,φ)-subdifferentiable functions, called (h,φ)-G-type I functions and generalized (h,φ)-G-type I functions. Then, we consider a class of nonconvex (h, φ)-subdifferentiable multiobjective programming problems with locally Lipschitz functions in which the functions involved belong to aforesaid classes of (h, φ)-subdifferentiable nonconvex functions. For such (h, φ)-subdifferentiable vector optimization problems, we prove the sufficient optimality conditions for a feasible solution to be its (weak) Pareto solution. Further, we define a vector dual problem in the sense of Mond-Weir for the considered (h, φ)-subdifferentiable multiobjective programming problem and we prove several duality theorems for the aforesaid (h, φ)-subdifferentiable vector optimization problems also under (h, φ)-G-type I hypotheses. [ABSTRACT FROM AUTHOR]

The growing use of optimization models to help decision making has created a demand for such tools that allow formulating and solving more models of real-world processes and systems related to human activity in which hypotheses are not verify in a way specific for classical optimization. One of the approaches for real-world extremum problems under uncertainty is interval-valued optimization. In this paper, a twice differentiable vector optimization problem with multiple interval-valued objective function and both inequality and equality constraints is considered. In this paper, the first order necessary optimality conditions of Karush-Kuhn-Tucker type are proved for differentiable interval-valued vector optimization problems under the first order constraint qualification. If the interval-valued objective function is assumed to be twice weakly differentiable and constraints functions are assumed to be twice differentiable, then two types of second order necessary optimality conditions under two various constraint qualifications are proved for such smooth interval-valued vector optimization problems. Finally, in order to illustrate the Karush-Kuhn-Tucker type necessary optimality conditions established in the paper, an example of an interval-valued optimization is given. [ABSTRACT FROM AUTHOR]

In this paper, two mathematical methods are used for solving a complex multicriteria optimization problem as the considered convex differentiable vector optimization problem with vanishing constraints. First of them is the linearized approach in which, for the original vector optimization problem with vanishing constraints, its associated multiobjective programming problem is constructed at the given feasible solution. Since the aforesaid multiobjective programming problem constructed in the linearized method is linear, one of the existing methods for solving linear vector optimization problems is applied for solving it. Thus, the procedure for solving the considered differentiable vector optimization problems with vanishing constraints is presented in the paper. [ABSTRACT FROM AUTHOR]

In this paper, the class of uncertain multi-dimensional fractional control problems with the first-order PDE constraints is investigated. The robust approach and the parametric method are applied for solving such control problems. Then, robust optimality is analyzed for the considered PDE-constrained multi-dimensional fractional control problem with uncertainty. Further, the exact absolute penalty function method is used for solving control problems created in both the aforementioned approaches. Then, under appropriate convexity hypotheses, exactness of the penalization of this exact penalty function method is investigated in the case when it is used for solving the considered control problem with uncertainty. Further, an algorithm based on the used method is presented, the main goal of which is to illustrate the precise steps to solve the unconstrained multi-dimensional non-fractional control problem with uncertainty associated with the constrained fractional control problem. [ABSTRACT FROM AUTHOR]

In this paper, in order to characterize optimality of a class of nonconvex differentiable multiobjective programming problems, we introduce two new types of vector variational-like inequalities, namely, a weak variational E-inequality and a vector variational E-inequality. Namely, under (strictly) E-convexity, we prove relationships between the aforesaid vector variational-like inequalities and differentiable vector optimization problems. Further, under (strictly) pseudo-E-convexity, we are in position to identify vector critical E-points, weak E-Pareto (E-Pareto) solutions of differentiable vector optimization problems and solutions of these introduced vector variational-like inequalities. [ABSTRACT FROM AUTHOR]

Optimization problems under uncertainty has achieved much attention because of inaccurate or incomplete data that often appear in real-world applications. In order to address this challenging issue, several types of methodologies have been developed in optimization theory and one of them is fuzzy optimization. In this paper, an attempt is taken to use the minimax exact penalty function method for solving convex nondifferentiable optimization problems with fuzzy objective functions and with both inequality and equality constraints. The most important property of exact penalty function methods, that is, exactness of the penalization, is defined and analyzed if the minimax penalty function method is applicable for solving a convex nondifferentiable optimization problem with a fuzzy objective function. It is proved that a (weak) KKT point of the considered fuzzy optimization problem is a (weakly) nondominated solution of its associated fuzzy penalized optimization problem constructed in the used penalized approach. Further, the conditions are also derived under which there is the equivalence between (weakly) nondominated solutions of the aforesaid fuzzy optimization problems. These results are established under assumption that the functions involved in the considered nondifferentiable fuzzy optimization problem are convex. Further, the algorithm of solving the considered nondifferentiable fuzzy optimization problem by using the minimax exact penalty fuzzy function method is proposed and its convergence is also established. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a nonconvex multitime control problem with first‐order PDE constraints is considered. Then, we investigate the absolute value exact penalty function method which is used for solving the aforesaid control problem. Namely, in order to ensure the effective use of the absolute value exact penalty function method in the considered case, the most important property of any exact penalty function method, that is, exactness of the penalization, is analyzed in the case when the aforementioned method is applied for solving the considered multitime control problem with first‐order PDE constraints in which the functionals involved are nonconvex. Thus, the equivalence between an optimal solution of the aforementioned control problem and a minimizer of its associated unconstrained multitime control problem constructed in the used absolute value exact penalty function method is proved under appropriate invexity hypotheses. [ABSTRACT FROM AUTHOR]

In this paper, a class of directionally differentiable multiobjective programming problems with inequality, equality and vanishing constraints is considered. Under both the Abadie constraint qualification and the modified Abadie constraint qualification, the Karush–Kuhn–Tucker type necessary optimality conditions are established for such nondifferentiable vector optimization problems by using the nonlinear version Gordan theorem of the alternative for convex functions. Further, the sufficient optimality conditions for such directionally differentiable multiobjective programming problems with vanishing constraints are proved under convexity hypotheses. Furthermore, vector Wolfe dual problem is defined for the considered directionally differentiable multiobjective programming problem vanishing constraints and several duality theorems are established also under appropriate convexity hypotheses. [ABSTRACT FROM AUTHOR]

This paper is devoted to introduce and investigate a new exact penalty function method which is called the l 1 exact penalty E-function method. Namely, we use the aforesaid exact penalty function method to solve a completely new class of nonconvex (not necessarily) differentiable mathematical programming problems, that is, E-differentiable minimization problems. Then, we analyze the most important from a practical point of view property of all exact penalty function methods, that is, exactness of the penalization. Thus, under appropriate E-convexity hypotheses, we prove the equivalence between the original E-differentiable extremum problem and its corresponding penalized optimization problem created in the introduced l 1 exact penalty E-function method. Further, we also present and investigate the algorithm for this exact penalty function method which minimizes the l 1 exact penalty E-function. The convergence theorem for the aforesaid algorithm is also established. [ABSTRACT FROM AUTHOR]

In the paper, we investigate a class of nondifferentiable semi-infinite multiobjective programming problems such that all functions constituting them are interval-valued. We derive both Fritz John necessary optimality conditions and, under a constraint qualification, Karush-Kuhn-Tucker necessary optimality conditions for (weak) $ LU $-Pareto solutions in the considered nondifferentiable semi-infinite vector interval-valued optimization problem. Under appropriate invexity hypotheses, we also prove sufficient optimality conditions for this semi-infinite interval-valued vector optimization problem. Further, we also use the $ l_{1} $ exact function method for solving the aforesaid nondifferentiable interval-valued multicriteria optimization problem. Then, we analyze the property of exactness of the penalization for the absolute value exact penalty function method under assumption that the functions involved in the considered semi-infinite multiobjective programming problem are locally Lipschitz interval-valued invex functions. The conditions guaranteeing the equivalence of the sets of (weak) $ LU $-Pareto solutions in the original semi-infinite interval-valued multiobjective programming problem and its associated vector penalized optimization problem with the multiple interval-valued $ l_{1} $ exact penalty function are given. [ABSTRACT FROM AUTHOR]

In this paper, we consider the class of nondifferentiable multiobjective fractional variational control problems involving the nondifferentiable terms in the numerators and in the denominators. Under univexity and generalized univexity hypotheses, we prove optimality conditions and various duality results for such nondifferentiable multiobjective fractional variational control problems. The results established in the paper generalize many similar results established earlier in the literature for such nondifferentiable multiobjective fractional variational control problems. [ABSTRACT FROM AUTHOR]

In this paper, by using the invexity (or pseudoinvexity) and Fréchet differentiability of some integral functionals of curvilinear type, we state some relations between the solutions of a new non-linear optimization problem and the associated variational inequality. In order to prove the results derived in this paper, we use the new notion of invex set by considering some given functions. To justify the effectiveness and outstanding applicability of this work, some illustrative examples are provided. [ABSTRACT FROM AUTHOR]

In this paper, the definitions of Clarke generalized directional α -derivative and Clarke generalized gradient are introduced for a locally Lipschitz fuzzy function. Further, a nonconvex nonsmooth optimization problem with fuzzy objective function and both inequality and equality constraints is considered. The Karush-Kuhn-Tucker optimality conditions are established for such a nonsmooth extremum problem. For proving these conditions, the approach is used in which, for the considered nonsmooth fuzzy optimization problem, its associated bi-objective optimization problem is constructed. The bi-objective optimization problem is solved by its associated scalarized problem constructed in the weighting method. Then, under invexity hypotheses, (weakly) nondominated solutions in the considered nonsmooth fuzzy minimization problem are characterized through Pareto solutions in its associated bi-objective optimization problem and Karush-Kuhn-Tucker points of the weighting problem. [ABSTRACT FROM AUTHOR]

In this paper, by considering some properties associated with scalar functionals of multiple-integral type, we study the well-posedness and generalized well-posedness for a new variational inequality-constrained optimization problems By using the set of approximating solutions, we state some characterization theorems on well-posedness and generalized well-posedness. Also, in order to validate the derived results, some examples are given. [ABSTRACT FROM AUTHOR]

In this paper, the convex nonsmooth optimization problem with fuzzy objective function and both inequality and equality constraints is considered. The Karush–Kuhn–Tucker necessary optimality conditions are proved for such a nonsmooth extremum problem. Further, the exact l 1 penalty function method is used for solving the considered nonsmooth fuzzy optimization problem. Therefore, its associated fuzzy penalized optimization problem is constructed in this approach. Then, the exactness property of the exact l 1 penalty function method is analyzed if it is used for solving the considered nonsmooth convex fuzzy optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions are proved for such nonconvex smooth vector optimization problems. Further, vector duals in the sense of Mond–Weir are defined for the considered differentiable semi-infinite multiobjective programming problems with vanishing constraints and several duality results are established also under invexity hypotheses. [ABSTRACT FROM AUTHOR]

In this paper, a differentiable vector optimization problem with the multiple interval-valued objective function and with both inequality and equality constraints is considered. The Karush-Kuhn-Tucker necessary optimality conditions are established for such a differentiable interval-valued multiobjective programming problem. Further, a new approach, called F-objective function method, is introduced for solving the considered differentiable vector optimization problem with the multiple interval-valued objective function. In this method, its associated vector optimization problem with the multiple interval-valued F-objective function is constructed. Their equivalence is established under F-convexity assumptions. It is shown that the introduced approach can be used to solve a nonlinear nonconvex interval-valued optimization problem. By using the introduced approximation method, it is also presented in some cases that a nonlinear nonconvex interval-valued optimization problem can be solved by the help of methods for solving linear interval-valued optimization problems. [ABSTRACT FROM AUTHOR]

In this paper, a new class of minimax programming problems is considered in which the functions involved are E-differentiable. The so-called parametric and nonparametric necessary E-optimality conditions are derived for the considered E-differentiable minimax programming problem. Further, sufficient optimality conditions are established for such nondifferentiable extremum problems under E-convexity hypotheses. Moreover, the example of a nonsmooth minimax programming problem with E-differentiable functions is given to illustrate the aforesaid results. Furthermore, the so-called Mond-Weir E-dual problem and Wolfe E-dual problem are defined for the considered E-differentiable minimax programming problem and several E-duality theorems are established also under appropriate E-convexity hypotheses. [ABSTRACT FROM AUTHOR]

Background: Microbial surfactants called biosurfactants, thanks to their high biodegradability, low toxicity and stability can be used not only in bioremediation and oil processing, but also in the food and cosmetic industries, and even in medicine. However, the high production costs of microbial surfactants and low efficiency limit their large-scale production. This requires optimization of management conditions, including the possibility of using waste as a carbon source, such as food processing by-products. This papers describes the production and characterization of the biosurfactant obtained from the endophytic bacterial strain Bacillus pumilus 2A grown on various by-products of food processing and its potential applications in supporting plant growth. Four different carbon and nitrogen sources, pH, inoculum concentration and temperature were optimized within Taguchi method. Results: Optimization of bioprocess within Taguchi method and experimental analysis revealed that the optimal conditions for biosurfactant production were brewer's spent grain (5% w/v), ammonium nitrate (1% w/v), pH of 6, 5% of inoculum, and temperature at 30 °C, leading to 6.8 g/L of biosurfactant. Based on gas chromatography–mass spectrometry and Fourier transform infrared spectroscopy analysis produced biosurfactant was determined as glycolipid. Obtained biosurfactant has shown high and long term thermostability, surface tension of 47.7 mN/m, oil displacement of 8 cm and the emulsion index of 69.11%. The examined glycolipid, used in a concentration of 0.2% significantly enhanced growth of Phaseolus vulgaris L. (bean), Raphanus L. (radish), Beta vulgaris L. (beetroot). Conclusions: The endophytic Bacillus pumilus 2A produce glycolipid biosurfactant with high and long tem thermostability, what makes it useful for many purposes including food processing. The use of brewer's spent grain as the sole carbon source makes the production of biosurfactants profitable, and from an environmental point of view, it is an environmentally friendly way to remove food processing by products. Glycolipid produced by endophytic Bacillus pumilus 2A significantly improve growth of Phaseolus vulgaris L. (bean), Raphanus L. (radish), Beta vulgaris L. (beetroot). Obtained results provide new insight to the possible use of glycolipids as plant growth promoting agents. [ABSTRACT FROM AUTHOR]

In this paper, a new approximation method for a characterization of (weak) Pareto solutions in some class of nonconvex differentiable multiobjective programming problems is introduced. In this method, an auxiliary approximated vector optimization problem is constructed at a given feasible solution of the original multiobjective programming problem. The equivalence between (weak) Pareto solutions of these two vector optimization problems is established under (Φ , ρ) -invexity hypotheses. By using the introduced approximation method, it is shown in some cases that a nonlinear differentiable multiobjective programming problem can be solved by the help of some methods for solving a linear vector optimization problem. Further, the introduced approximation method is used in proving several duality results in the sense of Mond-Weir for the considered vector optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, a nonconvex vector optimization problem with multiple interval-valued objective function and both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are E-differentiable. The so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable vector optimization problem with the multiple interval-valued objective function. Also the sufficient optimality conditions are derived for such interval-valued vector optimization problems under appropriate (generalized) E-convexity hypotheses. [ABSTRACT FROM AUTHOR]

In this article, we use the so-called η-approximation method for solving a new class of nonconvex variational problems with exponential (p, r)-invex functionals. In this approach, we construct η- approximated variational problem and η-approximated Mond- Weir dual variational problem for the considered variational problem and its Mond-Weir dual variational problem. Then several duality results for considered variational problem and its Mond-Weir dual variational problem are proved by the help of duality results established between η-approximated variational problems mentioned above. [ABSTRACT FROM AUTHOR]

In this paper, a nonconvex vector optimization problem with both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are E-differentiable. The so-called E-Fritz John necessary optimality conditions and the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable multiobjective programming problems with both inequality and equality constraints. Further, the sufficient optimality conditions are derived for such nonconvex nonsmooth vector optimization problems under (generalized) E-convexity. The so-called vector E-Wolfe dual problem is defined for the considered E-differentiable multiobjective programming problem with both inequality and equality constraints and several dual theorems are established also under (generalized) E-convexity hypotheses. [ABSTRACT FROM AUTHOR]

In this paper, a new approach to analyze optimality and saddle‐point criteria for a new class of nonconvex variational problems involving invex functions is studied. Namely, the modified objective function method is used for the considered variational problem in order to characterize its optimal solution. In this method, for the considered variational problem, corresponding modified variational problem with the η‐objective function is constructed. The equivalence in the original variational problem and its associated modified variational problem with the η‐objective function is proved under invexity hypotheses. Furthermore, by using the notion of a Lagrangian function, the connection between a saddle‐point in the modified objective function variational problem and an optimal solution in the considered variational problem is presented. Some examples of nonconvex variational problems are also given to verify the results established in the paper. [ABSTRACT FROM AUTHOR]

In this paper, the classical exact absolute value penalty function method is used for solving a new class of nonconvex nonsmooth optimization problems. Nonconvex nondifferentiable optimization problems with both inequality and equality constraints are considered here, in which not all functions constituting them have the fundamental property of convex functions and most classes of generalized convex functions—namely, a stationary point of such a function is its global minimum. It is proved for such nonconvex optimization problems that there exists a finite threshold of penalty parameters equal to the largest absolute value of a Lagrange multiplier such that, for every penalty parameter exceeding this lower bound, there is the equivalence between an optimal solution in the original constrained minimization problem with (Φ,ρ)‐invex functions and a minimizer in its associated penalized optimization problem with the exact l1 penalty function. Further, under nondifferentiable (Φ,ρ)‐invexity assumptions, a characterization of a saddle point of the Lagrange function, defined for the considered constrained optimization problem in terms of minimizers of its associated exact penalized optimization problem with the exact l1 penalty function, is presented. [ABSTRACT FROM AUTHOR]

In this paper, we use the modified objective function method for a class of nonconvex multiobjective variational problems involving univex functions. Under univexity hypotheses, we prove the equivalence between an (weakly) efficient solution of the considered multiobjective variational problem and an (weakly) efficient solution of the associated modified multiobjective variational problem constructed in the modified objective function method. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with optimality conditions and duality results for nondifferentiable multiobjective fractional programming problems. Parametric necessary optimality conditions are established for such vector optimization problems in which each component of the involved functions is locally Lipschitz. Further, under the introduced concept of nondifferentiable (b;Ψ,Φ,p-) -univexity, the parametric sufficient optimality conditions are established for a new class of nonconvex multiobjective fractional programming problems. Furthermore, for the considered multiobjective fractional programming problem, its parametric vector dual problem in the sense of Schaible is defined. Then several duality theorems are also established under (bΨ,Φ,p-univexity hypotheses. [ABSTRACT FROM AUTHOR]

The present paper is devoted to studying the modified objective function approach used for solving the considered multitime variational problem. In this method, a new multitime variational problem is constructed by modifying the objective function in the original considered multitime variational problem. Further, the equivalence between an optimal solution to the original multitime variational problem and its associated modified problem is established under both hypotheses of invexity and generalized invexity defined for a multitime functional. Thereafter, using the modified objective function method, we derive the saddle-point results for the considered multitime variational problem. Moreover, we provide some examples to illustrate the results established in the paper. [ABSTRACT FROM AUTHOR]

In this paper, a new vector exponential penalty function method for nondifferentiable multiobjective programming problems with inequality constraints is introduced. First, the case when a sequence of vector penalized optimization problems with vector exponential penalty function constructed for the original multiobjective programming problem is considered, and the convergence of this method is established. Further, the exactness property of a vector exact penalty function method is defined and analyzed in the context of the introduced vector exponential penalty function method. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto solutions of the considered nondifferentiable multiobjective programming problem and the associated vector penalized optimization problem with the vector exact exponential penalty function. This equivalence is established for nondifferentiable vector optimization problems with inequality constraints in which involving functions are r-invex. [ABSTRACT FROM AUTHOR]

In this paper, a new approximation method for a characterization of optimal solutions in a class of nonconvex differentiable optimization problems is introduced. In this method, an auxiliary optimization problem is constructed for the considered nonconvex extremum problem. The equivalence between optimal solutions in the considered differentiable extremum problem and its approximated optimization problem is established under (Φ; ρ)-invexity hypotheses. [ABSTRACT FROM AUTHOR]

In the paper, a necessary and sufficient criterion it provided such that any local optimal solution is also global in a not necessarily differentiable constrained optimization problem. This criterion is compared to others earlier appeared in the literature, which are sufficient but not necessary for a local optimal solution to be global. The importance of the established criterion is illustrated by suitable examples of nonconvex optimization problems presented in the paper. [ABSTRACT FROM AUTHOR]

Mucor circinelloidesIBT-83 mycelium that exhibits both lipolytic (AL) and chitosanolytic (ACH) activities was immobilized into polyurethane foam in a 30 L laboratory fermenter. The process of immobilization was investigated in terms of the carrier porosity, its type, amount, and shape, location inside the fermenter, mixing, and aeration parameters during the culture, as well as downstream processing operations. The selected conditions allowed for immobilization of approximately 7 g of defatted and dried mycelium in 1 g of carrier, i.e., seven times more than achievable in 1 L shake-flasks. Enzymatic preparation obtained by this method exhibited both the chitosanolytic (ACH432.5 ± 6.8 unit/g) and lipolytic (AL150.0 ± 9.3 U/g) activities. The immobilized preparation was successfully used in chitosan hydrolysis to produce chitooligosaccharides and low molecular weight chitosan, as well as in waste fats degradation and in esters synthesis in nonaqueous media. It was found that the half-life of immobilized preparations stored at room temperature is on average of 200 days. [ABSTRACT FROM PUBLISHER]

In this paper, we use the η-approximation method for a class of non-convex multiobjective variational problems with invex functionals. In this approach, for the considered multiobjective variational problem, the associated η-approximated multiobjective variational problem is constructed at the given feasible solution. The equivalence between (weakly) efficient solutions in the original multiobjective variational problem and its associated η-approximated multiobjective variational problem is established under invexity hypotheses. [ABSTRACT FROM AUTHOR]

The objective of presented study was to maximize yields of 2-methylbutyl esters, derived by transesterification reactions mediated by sn-1,3-specific lipases, through engineering of reaction medium. Effects of water and diethylamine (DEA) concentrations on the efficiency of plant oils 2-methylbutanolysis, catalyzed by either mycelium-boundMucor circinelloideslipase (powder) or commercial immobilized lipase Lipozyme TL IM, were determined. Water content monitoring in reaction mixtures enabled to optimize the initial water content in terms of preventing the dehydration of enzyme’s microenvironment and increasing 2-methylbutyl esters yields. These yields were found to be increased by addition of either suitable amounts of water (0.5–1.5%) or diethylamine (10–30 mM) to the mixture of substrates. The presented results suggest that at low concentrations, diethylamine molecules contribute to retaining water in the microenvironment of enzyme that gives rise to increased transesterification yields and significantly reduced amounts of residual mono- and 1,2-diacyl-glycerols. [ABSTRACT FROM PUBLISHER]

In this article, the vector exact l1 penalty function method used for solving nonconvex nondifferentiable multiobjective programming problems is analyzed. In this method, the vector penalized optimization problem with the vector exact l1 penalty function is defined. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penalized optimization problem with the vector exact l1 penalty function. This equivalence is established for nondifferentiable invex vector optimization problems. Some examples of vector optimization problems are presented to illustrate the results established in the article. [ABSTRACT FROM AUTHOR]

In this paper, it is demonstrated that the exact absolute value penalty function method is useful for identifying the special sort of minimizers in nonconvex nonsmooth optimization problems with both inequality and equality constraints. The equivalence between the sets of strict global minima of order m in nonsmooth minimization problem and of its associated penalized optimization problem with the exact $$l_{1}$$ penalty function is established under nondifferentiable $$\left( F,\rho \right) $$ -convexity assumptions imposed on the involved functions. The threshold of the penalty parameter, above which this result holds, is also given. [ABSTRACT FROM AUTHOR]

In this paper, we consider a multitime multiobjective fractional variational problem of minimizing a vector of quotients of path-independent curvilinear integral functionals subject to certain partial differential equations and inequations. Using the so-called parametric approach, we establish necessary and sufficient optimality conditions for the considered class of multitime multiobjective fractional variational problems under both ( F, ρ)-convexity and generalized ( F, ρ)-convexity. Further, the parametric multiobjective variational dual problem is formulated for the considered multitime multiobjective fractional variational problem, and several duality results are established under (generalized) ( F, ρ)-convexity. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with directionally differentiable functions is considered. The so-called G-V-type I objective and constraint functions and their generalizations are introduced for such nonsmooth vector optimization problems. Based upon these generalized invex functions, necessary and sufficient optimality conditions are established for directionally differentiable multiobjective programming problems. Thus, new Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions are proved for the considered directionally differentiable multiobjective programming problem. Further, weak, strong and converse duality theorems are also derived for Mond-Weir type vector dual programs. [ABSTRACT FROM AUTHOR]

Chitosan is a linear N-deacetylated derivative of chitin, soluble in acetic solutions. The deacetylation of chitin can be achieved enzymatically using chitin deacetylase (ChDa) (EC 3.5.1.41), which hydrolyses the N-acetamido groups of N-acetyl-D-glucosamine residues in chitin and chitosan. Complementary DNA (cDNA), which encodes ChDa, was isolated from M. rouxii s well as other fungi. Chitin deacetylase activity was detected in partially purified and concentrated crude extract of the protein from Mucor circinelloides IBT-83. Additionally, two open reading frames (ORF), putatively encoding ChDa, were identified and amplified from cDNA of this strain. Each ORF was molecularly cloned and sequenced. Amino acid sequences of ChDaI and ChDaII were predicted, using nucleotide sequences of these cDNA clones, and analysed by means of bioinformatics tools. [ABSTRACT FROM AUTHOR]

In this paper, saddle point criteria and Wolfe duality theorems are established for a new class of nondifferentiable vector optimization problems with inequality and equality constraints. The results are proved under nondifferentiable (Φ, ρ)-invexity and related scalar and vector-valued Lagrangians defined for the considered nonsmooth multiobjective programming problem. It turns out that the results are established for such vector optimization problems in which not all functions constituting a vector optimization problem possess the fundamental property of invexity and the most of generalized invexity notions previously defined in the literature. [ABSTRACT FROM PUBLISHER]

In the paper, we introduce the concepts of $$G$$ -type I and generalized $$G$$ -type I functions for a new class of nonconvex multiobjective variational control problems. For such nonconvex vector optimization problems, we prove sufficient optimality conditions for weakly efficiency, efficiency and properly efficiency under assumptions that the functions constituting them are $$G$$ -type I and/or generalized $$G$$ -type I objective and constraint functions. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem is given and several duality results are established under (generalized) $$G$$ -type I objective and constraint functions. [ABSTRACT FROM AUTHOR]

A semi-infinite minimax fractional programming problem with both inequality and equality constraints is considered. Characterizations of an optimal solution by a saddle point of the scalar Lagrange function and the vector-valued Lagrange function defined for such an optimization problem are given. Hence, the equivalence between an optimal solution and a saddle point of the scalar Lagrange function and the vector-valued Lagrange function in the considered semi-infinite minmax fractional programming problem is established under various (p,r)-invexity assumptions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of KT-G-invexity and WD-G-invexity for the considered differentiable optimization problem with inequality constraints. Using KT-G-invexity notion, we prove new necessary and sufficient optimality conditions for a new class of such nonconvex differentiable optimization problems. Further, the so-called G-Wolfe dual problem is defined for the considered extremum problem with inequality constraints. Under WD-G-invexity assumption, the necessary and sufficient conditions for weak duality between the primal optimization problem and its G-Wolfe dual problem are also established. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the notion of B-(p, r)-invexity introduced by Antczak in [A class of B-(p; r)-invex functions and mathematical programming, J. Math. Anal. Appl. 286 (2003), 187-206] for scalar optimization problems to the case of a multiobjective variational programming control problem. For such nonconvex vector optimization problems, we prove sufficient optimality conditions under the assumptions that the functions constituting them are B-(p, r)-invex. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem in the sense of Mond-Weir is given and several duality results are established under B-(p, r)-invexity. [ABSTRACT FROM AUTHOR]

In this paper, Mond-Weir and Wolfe type duals for multiobjective variational control problems are formulated. Several duality theorems are established relating efficient solutions of the primal and dual multiobjective variational control problems under $$(\Phi , \rho )$$ -invexity. The results generalize a number of duality results previously established for multiobjective variational control problems under other generalized convexity assumptions. [ABSTRACT FROM AUTHOR]

In this paper, a new class of generalized of nonconvex multitime multiobjective variational problems is considered. We prove the sufficient optimality conditions for efficiency and proper efficiency in the considered multitime multiobjective variational problems with univex functionals. Further, for such vector variational problems, various duality results in the sense of Mond-Weir and in the sense of Wolfe are established under univexity. The results established in the paper extend and generalize results existing in the literature for such vector variational problems. [ABSTRACT FROM AUTHOR]

In this paper, we extend the notions of $$(\Phi ,\rho )$$ -invexity and generalized $$(\Phi ,\rho )$$ -invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvex multiobjective variational control problems. Further, multiobjective variational control mixed dual problem is given for the considered multiobjective variational control problem and several mixed duality results are established under $$(\Phi ,\rho )$$ -invexity. [ABSTRACT FROM AUTHOR]