This paper is concerned with the semi-infinite programming problems with vanishing constraints. Both necessary and sufficient Karush-Kuhn-Tucker optimality conditions for the semi-infinite programming problems with va...
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This paper is concerned with the semi-infinite programming problems with vanishing constraints. Both necessary and sufficient Karush-Kuhn-Tucker optimality conditions for the semi-infinite programming problems with vanishing constraints are established. We also formulate types of Wolfe and Mond-Weir dual problems and explore duality relations under convexity assumptions. Some examples are given to illustrate our results.
In this paper, we focus on the lower bounds of the L-p is an element of(p [1,infinity), p =infinity) induced norms of continuous-time LTI systems where input signals are restricted to be nonnegative. This induced norm...
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ISBN:
(纸本)9781713872344
In this paper, we focus on the lower bounds of the L-p is an element of(p [1,infinity), p =infinity) induced norms of continuous-time LTI systems where input signals are restricted to be nonnegative. This induced norm, called the Lp+ induced norm, is particularly useful for the stability analysis of nonlinear feedback systems constructed from linear systems and static nonlinearities where the nonlinearities provide only nonnegative signals for the case p = 2. To have deeper understanding on the Lp+ induced norm, we analyze its lower bounds with respect to the standard L-p induced norm in this paper. As the main result, we show that the Lp+ induced norm of an LTI system cannot be smaller than the L-p induced norm scaled by 2((1- p)/p) for is an element of[1,infinity) (scaled by 2(-1) for p =infinity). On the other hand, in the case where p = 2, we further propose a method to compute better (larger) lower bounds for single- input systems via reduction of the lower bound analysis problem into a semi-infiniteprogramming problem. The effectiveness of the lower bound computation method, together with an upper bound computation method proposed in our preceding paper, is illustrated by numerical examples. Copyright (c) 2023 The Authors.
In this paper, we focus on the lower bounds of the L p ( p ∈ [1 ,∞ ) , p = ∞ ) induced norms of continuous-time LTI systems where input signals are restricted to be nonnegative. This induced norm, called the L p + ...
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In this paper, we focus on the lower bounds of the L p ( p ∈ [1 ,∞ ) , p = ∞ ) induced norms of continuous-time LTI systems where input signals are restricted to be nonnegative. This induced norm, called the L p + induced norm, is particularly useful for the stability analysis of nonlinear feedback systems constructed from linear systems and static nonlinearities where the nonlinearities provide only nonnegative signals for the case p = 2. To have deeper understanding on the L p + induced norm, we analyze its lower bounds with respect to the standard L p induced norm in this paper. As the main result, we show that the L p + induced norm of an LTI system cannot be smaller than the L p induced norm scaled by 2 (1 -p ) /p for ∈ [1 ,∞ ) (scaled by 2 − 1 for p = ∞ ). On the other hand, in the case where p = 2, we further propose a method to compute better (larger) lower bounds for single-input systems via reduction of the lower bound analysis problem into a semi-infiniteprogramming problem. The effectiveness of the lower bound computation method, together with an upper bound computation method proposed in our preceding paper, is illustrated by numerical examples.
The present paper is concerned with a general approach for the construction of stable methods solving convex variational problems. This approach uses the procedure of iterative PROX-regularization in connection with s...
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The present paper is concerned with a general approach for the construction of stable methods solving convex variational problems. This approach uses the procedure of iterative PROX-regularization in connection with suitable methods of sequential discretizations of convex variational inequalities and semi-infinite programming problems. The presented investigation scheme for such methods allows to establish conditions which control the behaviour of the methods and guarantee the strong convergence of the obtained minimizing sequence. The possibility of realizing of this scheme is described for some concrete elliptical variational inequalities and also for some numerical algorithms, where the parameters of discretization and of convergence controlling are coordinated.
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