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The composite vector function is introduced, which is applied to multiobjective programming with equality constraints and inequality constraints, three theorems on the optimality sufficient condition are established in this article. on the Banach space,optimality of composite function and pseudoconvex and strictly pseudo-convex of composite function are redefined. We introduce Jacobian matrix and...
Let C be a closed bounded convex subset of a Banach space X with 0 being an interior point of C and pC(.) be the Minkowski functional with respect to C. A generalized mutually maximization problem is said to be well posed if it has a unique solution (x, z) and every maximizing sequence converges strongly to (x, z). Under the assumption that the modulus of convexity with respect to pC(.) is strictly...
Let C be a closed bounded convex subset of a Banach space X with 0 being an interior point of C and pC (.) be the Minkowski functional with respect to C. A generalized mutually maximization problem maxC (F, G) is said to be well posed if it has a unique solution (x, z) and every maximizing sequence converges strongly to (x, z). Under the assumption that C is both strictly convex and Kadec, G is a...
The moment problem matured from its various special forms in the late 19th and early 20th Centuries to a general class of problems that continues to exert profound influence on the development of analysis and its applications to a wide variety of fields. In particular, the theory of systems and control is no exception, where the applications have historically been to circuit theory, optimal control,...
Let C be a closed bounded convex subset of a Banach space X with 0 being an interior point of C and pC(.) be the Minkowski functional with respect to C. Let B(X) be the family of nonempty bounded closed subset of X endowed with the Hausdorff distance. A generalized mutually minimization problem minC(F,G) is said to be well posed if it has a unique solution (x. z) and every minimizing sequence converges...
As well known, the Moreau-Rockafellar-Robinson internal point qualification condition is sufficient to ensure that the infimal convolution of the conjugates of two extended-real-valued convex lower semi-continuous functions defined on a locally convex space is exact, and that the subdifferential of the sum of these functions is the sum of their subdifferentials. This note is devoted to proving that...
This paper presents a new implementable algorithm for solving the Lipschitz classifier that is a generalization of the maximum margin concept from Hilbert to Banach spaces. In contrast to the support vector machine approach, our algorithm is free to use any finite family of continuously differentiable functions which linearly compose the decision function. Nevertheless, robustness properties are maintained...
This paper deals with approximate value iteration (AVI) algorithms applied to discounted dynamic (DP) programming problems. The so-called Bellman residual is shown to be convex in the Banach space of candidate solutions to the DP problem. This fact motivates the introduction of an AVI algorithm with local search that seeks an approximate solution in a lower dimensional space called approximation architecture...
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