[PDF] Top 20 Duality for a Control Problem Involving Support Functions

... type duality for a control problem having support functions is studied under generalized convexity ...programming problem with support functions is indicated. The ... See full document

... Proof Since x ∗ is an optimal solution for (P) and all the conditions of Theorem . are satisfied, there exist (s ∗ , λ ∗ , y ∗ ) ∈ K , and (x ∗ , μ ∗ ) ∈ H (s ∗ , λ ∗ , y ∗ ) such that (x ∗ , μ ∗ , s ∗ , λ ∗ , y ∗ ) is ... See full document

... of functions or diverse ...nondifferentiable functions and also established the du- ality ...and duality for non-smooth, non-linear multiobjective fractional programming ...the duality results ... See full document

... [10] Yan, C.L. and Feng, B.C. (2015) Sufficiency and Duality for Nonsmooth Multiob- jective Programming Problems Involving Generalized ( , ) ϕ ρ -V-Type I Functions. Journal of Mathematical Modelling ... See full document

... optimal control problem and presented the weak, strong and converse duality ...and duality theorems for frac- tional generalized minimax programming problem are ...the functions ... See full document

... and duality for non- linear programming ...These functions were named invex by Craven ...and duality for multiobjective programming problems are discussed in [14], and inseparable Hilbert spaces are ... See full document

... of functions by genera- lizing the difference vector x  x in the definition of a convex function to any vector function   x x ,  ...These functions were named invex by Craven [2] and  -con- vex by Kaul ... See full document

... invex functions, called generalized V-type I invex functions, an extension of V- type I functions introduced by Hanson et ...type duality relations for nonsmooth multiobjective programming ... See full document

... problems involving new classes of generalized B-(p, r)- type I ...appropriate duality theorems in the setting of Mond-Weir type dual are also presented in order to relate the efficient solutions of primal ... See full document

... strong duality theorems were established under second order F-convexity assump- ...cone-pseudoinvex functions, and formulated a pair of Mond-Weir type symmetric dual multiobjective programs over arbitrary ... See full document

... dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is ...converse ... See full document

... Proof: Since ( x u , ) is an optimal solution of (CP) and is normal, by Theorem 1, it implies that there exist piecewise smooth λ j : I → R , j = 1, 2,  , m , u I : → R n , z I : → R n and ω j : I → R n ( j = 1, 2,  , ... See full document

... the support functions and inner prod- ucts in the problems (NFVP) and (NFVD) in the draft disappear, and hence (NFVP) and (NFVD) in the draft collapse to (P) and (D) in the paper of Ahmad, Sharma (EJOR, ... See full document

... Order Duality in Mul- tiobjective Fractional Programming with Support ...(2016) Duality for a Nondifferentiable Multiobjective Higher-Order Symmetric Fractional Programming Problems with Cone Con- ... See full document

... equilibrium problem (GNEP for short) is an extension of the clas- sical Nash equilibrium problem, in which each player’s strategy set depends on the ri- val player’s ... See full document

... in control of robots [], transportation theory [], eigenvalue computations [], wavelet filter design [, ], statistical design [], ...etc. Duality of semi-infinite programming arises in the theory of ... See full document

... optimal control problem when the gradient information is not ...new control parameterization based on Bernstein basis functions is suggested to convert control problem into ... See full document

... in control engineering from the East China Petroleum Insti- tute, Dongying, China, in 1982, and a PhD de- gree in control engineering from the City Univer- sity at London in ... See full document

... Bent functions are maximally nonlinear Boolean ...important functions introduced by Rothaus and studied firstly by Dillon and next by many re- searchers for four ...bent functions seems elusive, many ... See full document

... While graphing technology makes it easy to plot the graph of a product function directly, it can sometimes be useful to plot the graphs of the individual functions f and g, particularly when one of the ... See full document