Proximal Analysis and Minimization Principles
نویسندگان
چکیده
منابع مشابه
A Proximal Minimization Algorithm for Constrained Optimization
The proximal minimization algorithm (PMA) is an iterative method for minimizing a convex function f(x) over D, the closure of the essential domain of a second convex function h. The PMA is an interior-point algorithm, in the sense that each iterate lies within the interior of D. For each k, the next iterate, x, minimizes the function f(x) +Dh(x, x ), where Dh(x, z) = h(x)− h(z)− 〈∇h(z), x− z〉 i...
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In this paper, we propose an alternating proximal gradient method that solves convex minimization problems with three or more separable blocks in the objective function. Our method is based on the framework of alternating direction method of multipliers. The main computational effort in each iteration of the proposed method is to compute the proximal mappings of the involved convex functions. T...
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We consider an extension of the proximal minimization algorithm where only some of the minimization variables appear in the quadratic proximal term. We interpret the resulting iterates in terms of the iterates of the standard algorithm and we show a uniform descent property, which holds independently of the proximal terms used. This property is used to give simple convergence proofs of parallel...
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In this paper we investigate the applicability of a recently introduced primal-dual splitting method in the context of solving portfolio optimization problems which assume the minimization of risk measures associated to different convex utility functions. We show that, due to the splitting characteristic of the used primal-dual method, the main effort in implementing it constitutes in the calcu...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1995
ISSN: 0022-247X
DOI: 10.1006/jmaa.1995.1436