Titlebook: Vector Optimization and Monotone Operators via Convex Duality; Recent Advances Sorin-Mihai Grad Book 2015 Springer International Publishing

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Vector Optimizationhttp://image.papertrans.cn/v/image/980844.jpg

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https://doi.org/10.1007/978-3-319-08900-3Conjugacy; Duality; Monotone operators; Representative functions; Vector optimization

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Sorin-Mihai GradPresents the first approach to the maximal monotonicity of the diagonal operators by means of representative functions.Introduces a framework for vector duality via general scalarizations.Investigates

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Introduction and Preliminaries,ity and other methods of the convex analysis. This is not intended to be a systematic presentation of the state-of-the-art in these fields, but an extended collection of the results obtained by the author in these research areas by making use of tools like conjugate functions, duality and convexity.

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Introduction and Preliminaries,ity and other methods of the convex analysis. This is not intended to be a systematic presentation of the state-of-the-art in these fields, but an extended collection of the results obtained by the author in these research areas by making use of tools like conjugate functions, duality and convexity.

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Duality for Scalar Optimization Problems,over, if . can be proven, the optimal objective values of the two problems coincide and they can be determined since usually the dual problem has a simpler structure than the primal one and can be easier solved. Moreover, necessary and sufficient . for the primal-dual pair of problems in discussion

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Vector Duality via Scalarization for Vector Optimization Problems, purposes, among which one can find the theory of vector optimization. Solving a vector optimization problem amounts of determining its feasible elements where the value of its objective function satisfies the desired minimality property within the image set of the feasible set through the objective

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Book 2015r linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering