Vector optimization problems

Lecture Artificial intelligence: Support vector machine. This lecture provides students with content including: distance from a point to a line/plane/hyperplane; equal margins; largest margins; optimization problem;... Please refer to the detailed content of the lecture!

7p codabach1016 03-05-2024 0 0   Download

Ebook "Application of computational intelligence to biology" is a contribution of translational and allied research to the proceedings of the International Conference on Computational Intelligence and Soft Computing. It explains how various computational intelligence techniques can be applied to investigate various biological problems. It is a good read for Research Scholars, Engineers, Medical Doctors and Bioinformatics researchers.

107p duongthandue0501 28-02-2024 3 1   Download

Fritz John necessary conditions for local Henig and global efficient solutions of vector equilibrium problems involving equality, inequality and set constraints with nonsmooth functions are established via convexificators. Under suitable constraint qualifications, Kuhn–Tucker necessary conditions for local Henig and gobally efficient solutions are derived.

19p vioracle 25-09-2023 2 2   Download

Lecture Convex optimization - Chapter: Convex optimization problems. This chapter presents the following content: Optimization problem in standard form, convex optimization problems, quasiconvex optimization, linear optimization, quadratic optimization, geometric programming, generalized inequality constraints, semidefinite programming, vector optimization.

47p runthenight09 16-05-2023 5 3   Download

In this section, we recall some notations and properties of differentiable convex functions, differentiable functions that the gradient vectors are Lipschitz contiuous. These notations and properties are used in the proofs of main results in this paper.

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Nonconvex SINR constraints in amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay beamforming problems make the design mathematically intractable. A more practical optimization is to maximize the minimum SINR achievable data rate among all the users. The previously existing methods invoke the vectorization of pre-coding matrix X and then introduce the auxiliary variable matrix of lager dimension which results in an increased computational complexity.

5p viericschmid 12-01-2022 14 2   Download

In this paper we propose results on zero duality gap in vector optimization problems posed in a real locally convex Hausdorff topological vector space with a vector-valued objective function to be minimized under a set and a convex cone constraint. These results are then applied to linear programming.

14p nguaconbaynhay12 03-06-2021 13 1   Download

The search for optimum design variables is conducted by using a recent heuristic method, namely Grey Wolf Optimizer. During the heuristic search, direct heat conduction problem has to be solved several times. The set of heat transfer parameters that lead to smallest error rate between computed temperature field and reference one is the optimum output of the inverse problem. In order to accelerate the process, the model order reduction technique Proper-Orthogonal-Decomposition (POD) is used.

14p nguaconbaynhay11 07-04-2021 15 3   Download

In this paper, we study a concept on the calm B-differentiability, a new kind of generalized differentiabilities for a given vector function introduced by Ye and Zhou in 2017, of the projector onto the circular cone. Then, we discuss its applications in mathematical programming problems with circular cone complementarity constraints. Here, this problem can be considered to be a generalization of mathematical programming problems with second-order cone complementarity constraints, and thus it includes a large class of mathematical models in optimization theory.

10p trinhthamhodang9 04-12-2020 14 4   Download

The concept of approximation introduced by D.T. Luc et al. [1] as a generalized derivative for non-Lipschitz vector functions to consider vector problems with non-Lipschitz data under inclusion constraints. Some calculus of approximations are presented. A necessary optimality condition, a type of KKT condition, for local efficient solutions of the problems is established under an assumption on regularity. Applications and numerical examples are also given.

11p nguaconbaynhay9 03-12-2020 14 1   Download

Bài giảng "Máy học nâng cao: Support vector machine" cung cấp cho người học các kiến thức: Introduction, review of linear algebra, classifiers & classifier margin, linear svms - optimization problem, hard vs soft margin classification, non linear svms. Mời các bạn cùng tham khảo.

77p abcxyz123_08 11-04-2020 40 4   Download

Lack of coordination between network layers limits the performance of most proposed solution for new challenges posed by wireless networks. To overcome such limitations, cross-layer physical and medium access (PHY-MAC) design for multi-input-multi-output orthogonal frequency division multiple access system in heterogeneous networks (HetNETs) is proposed. In this paper, we formulate an optimization problem for hybrid beamforming, in a multi-user HetNET scenario aiming to maximize the total system throughput.

8p son248 24-03-2020 21 2   Download

The purpose of this paper is to present a new and an alternative differential evolution (ADE) algorithm for solving unconstrained global optimization problems. In the new algorithm, a new directed mutation rule is introduced based on the weighted difference vector between the best and the worst individuals of a particular generation. The mutation rule is combined with the basic mutation strategy through a linear decreasing probability rule. This modification is shown to enhance the local search ability of the basic DE and to increase the convergence rate.

17p kethamoi1 17-11-2019 20 1   Download

In this paper, we propose an efficient method for solving the kinematic problem for asymmetrical parallel manipulators. By solving, we converted the kinematic problem to the optimal form. Mathematical models are obtained by using loop of vector equation as other parallel manipulators.

10p visumika2711 17-07-2019 13 1   Download

Research optimality conditions for local weak efficient solution in vector equilibrium problem involving set, inequality and equality constraints with stable functions via contingent derivatives in finite-dimensional spaces. Research optimality conditions for weak, Henig, global and superefficient solutions in vector equilibrium problems with steady. Research second order optimality conditions for weak, Henig, global, super-efficient solutions in vector equilibrium problems with arbitrary functions in terms of contingent epiderivatives in Banach spaces.

26p xacxuoc4321 11-07-2019 16 4   Download

In this paper the notion of Strict Benson proper-ε-efficient solution for a vector optimization problem with set-valued maps is introduced. The scalarization theorems and ε-Lagrangian multiplier theorems are established under the assumption of ic-cone-convexlikeness of set-valued maps.

9p vinguyentuongdanh 19-12-2018 24 0   Download

In this paper we introduce a notion of minimal solutions for set-valued optimization problem in terms of improvement sets by unifying a solution notion, introduced by Kuroiwa for set-valued problems, and a notion of optimal solutions in terms of improvement sets, introduced by Chicco et al for vector optimization problems. We provide existence theorems for these solutions, and establish lower convergence of the minimal solution sets in the sense of Painlev´e-Kuratowski.

15p danhnguyentuongvi27 19-12-2018 13 1   Download

We examine the first phase of a known NP-hard 2-stage assembly problem. It consists of sequencing a set of jobs having multiple components to be processed. Each job has to be worked on independently on a specific machine. We consider these jobs to form a vector of tasks. Our objective is to schedule jobs on the particular machines in order to minimize the completion time before the second stage starts.

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We present some duality theorems for a non-smooth Lipschitz vector optimization problem. Under generalized invexity assumptions on the functions the duality theorems do not require constraint qualifications.

7p vinguyentuongdanh 19-12-2018 32 0   Download

In this paper, we establish some existence theorems for vector quasiequilibrium problems in real locally convex Hausdorff topological vector spaces by using Kakutani-Fan-Glicksberg fixedpoint theorem. Moreover, we also discuss the closedness of the solution sets for these problems. The results presented in the paper are new and improve some main results in the literature.

10p danhvi10 22-11-2018 27 0   Download