Duality theorems

Continued part 1, part 2 of ebook "Linear algebra" has presents the following content: linear forms and bilinear forms; euclidean and unitary vector spaces; adjoints of linear maps; eigenvalues of endomorphisms; polynomials and the fundamental theorem of algebra; cyclic subspaces, duality and the jordan canonical form; matrix functions and systems of differential equations; special classes of endomorphisms; the singular value decomposition; the kronecker product and linear matrix equations;...

164p dieptieuung 20-07-2023 4 3   Download

In the present paper, we introduce a pair of second order fractional symmetric variational programs over cone constraints and derive weak, strong, and converse duality theorems under second order F-convexity assumptions. Moreover, self duality theorem is also discussed. Our results give natural unification and extension of some previously known results in the literature.

19p danhnguyentuongvi27 19-12-2018 22 0   Download

A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r) − ρ − (η,θ) - invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved.

20p vinguyentuongdanh 19-12-2018 26 1   Download

In this paper, we consider a nonsmooth semi-infinite multiobjective programming problem involving support functions. We establish sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak, strong and strict converse duality theorems under various generalized convexity assumptions. Moreover, some special cases of our problem and results are presented.

14p danhnguyentuongvi27 19-12-2018 20 1   Download

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

Following a brief introduction and overview, early chapters cover the basic algebraic relationships of entropy, relative entropy and mutual information, AEP, entropy rates of stochastics processes and data compression, duality of data compression and the growth rate of wealth. Later chapters explore Kolmogorov complexity, channel capacity, differential entropy, the capacity of the fundamental Gaussian channel, the relationship between information theory and statistics, rate distortion and network information theories.

0p hiepkhach_1006 10-09-2013 67 6   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Optimality and Duality Theorems in Nonsmooth

11p dauphong12 07-02-2012 30 2   Download

This note gives a new proof of the theorem, due to Ingleton and Pi [3], that the duals of transversal matroids are precisely the strict gammoids. Section 1 denes the relevant objects. Section 2 presents explicit representations of the families of transversal matroids and strict gammoids. Section 3 uses these representations to prove the duality of these two families.

6p thulanh6 14-09-2011 54 3   Download