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Elements of Convex Analysis. Linear Theorems of the Alternative. Tangent Cones, convex sets and convex cones. Convex functions and generalized convex functions will be discussed in the next chapter. Geometrically, a set . is .if the line segment joining any two points in the set lies entirely in the set. We recall that the (closed) line segment joining the points . and . of .,LIMN 发表于 2025-3-22 04:14:34
Sensitivity Analysis,lems. In many applications, the objective function ., as well as the constraints . . and . . may depend also on certain number of parameters. For some of these applications the optimal solution . of the unperturbed problem (i.e. with fixed values of the parameters) may be of less interest than itsaggrieve 发表于 2025-3-22 08:17:47
Convex Optimization: Saddle Points Characterization and Introduction to Duality, variations or optimal control) where the functions involved are not differentiable (in the sense of Fré chet), but satisfy weaker assumptions concerning various kinds of limits in various kinds of differential quotients, in order to obtain generalized gradients or generalized directional derivative口诀法 发表于 2025-3-22 12:00:08
Linear Programming and Quadratic Programming,fine) constraints. Usually, the variables are also required to be nonnegative. As L. P. is a particular case of nonlinear programming (the involved functions are both convex and concave and differentiable on .), all theorems seen for the general case of nonlinear programming hold also for L. P. andinfantile 发表于 2025-3-22 13:50:11
Introduction to Nonsmooth Optimization Problems,zation of saddle points of the Lagrangian function, in Chap. .) that the functions involved in the said problems are differentiable or continuously differentiable or twice-continuously differentiable. Starting from the 70s of the last century, the necessity of studying nonsmooth (i.e. nondifferentia表两个 发表于 2025-3-22 20:31:57
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https://doi.org/10.1007/978-1-4614-4499-2In the present chapter, we are concerned with constrained optimization problems with inequality constraints, i.e. with problem ..