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445
Semismoothness of solutions to generalized equations and the Moreau–Yosida regularization
 Math. Programming
"... We show that a locally Lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point. We present a sufficient condition for the semismoothness of solutions to generalized equations over cone reducible (nonpolyhedral) convex sets. ..."
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Cited by 27 (14 self)
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. We prove that the semismoothness of solutions to the MoreauYosida regularization of a lower semicontinuous proper convex function is implied by the semismoothness of the metric projector over the epigraph of the convex function.
MoreauYosida Regularization for Grouped Tree Structure Learning
"... We consider the tree structured group Lasso where the structure over the features can be represented as a tree with leaf nodes as features and internal nodes as clusters of the features. The structured regularization with a predefined tree structure is based on a groupLasso penalty, where one grou ..."
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Cited by 33 (7 self)
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. In this paper, we develop an efficient algorithm for the tree structured group Lasso. One of the key steps in the proposed algorithm is to solve the MoreauYosida regularization associated with the grouped tree structure. The main technical contributions of this paper include (1) we show that the associated
On Secondorder Properties of the MoreauYosida Regularization for Constrained Nonsmooth Convex Programs
"... In this paper, we attempt to investigate a class of constrained nonsmooth convex optimization problems, that is, piecewise C 2 convex objectives with smooth convex inequality constraints. By using the MoreauYosida regularization, we convert these problems into unconstrained smooth convex programs. ..."
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Cited by 1 (0 self)
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In this paper, we attempt to investigate a class of constrained nonsmooth convex optimization problems, that is, piecewise C 2 convex objectives with smooth convex inequality constraints. By using the MoreauYosida regularization, we convert these problems into unconstrained smooth convex programs
Practical Aspects of the MoreauYosida Regularization I: Theoretical Properties
, 1994
"... When computing the infimal convolution of a convex function f with the squared norm, one obtains the socalled MoreauYosida regularization of f . Among other things, this function has a Lipschitzian gradient. We investigate some more of its properties, relevant for optimization. Our main result co ..."
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Cited by 65 (2 self)
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When computing the infimal convolution of a convex function f with the squared norm, one obtains the socalled MoreauYosida regularization of f . Among other things, this function has a Lipschitzian gradient. We investigate some more of its properties, relevant for optimization. Our main result
On Smoothness of the MoreauYosida Regularization of a Lagrangiandual Function
"... In this paper we consider the Lagrangiandual of a class of optimization problems. First we discuss the piecewise smoothness of the Lagrangiandual function phi. This property is then used to investigate the secondorder properties of the MoreauYosida regularization eta of the function phi. We show ..."
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Cited by 2 (0 self)
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In this paper we consider the Lagrangiandual of a class of optimization problems. First we discuss the piecewise smoothness of the Lagrangiandual function phi. This property is then used to investigate the secondorder properties of the MoreauYosida regularization eta of the function phi. We
On the MoreauYosida regularization of the vector knorm related functions
, 2011
"... In this paper, we conduct a thorough study on the first and second order properties of the MoreauYosida regularization of the vector knorm function, the indicator function of its epigraph, and the indicator function of the vector knorm ball. We start with settling the vector knorm case via apply ..."
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Cited by 4 (2 self)
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In this paper, we conduct a thorough study on the first and second order properties of the MoreauYosida regularization of the vector knorm function, the indicator function of its epigraph, and the indicator function of the vector knorm ball. We start with settling the vector knorm case via
A MoreauYosida regularization of a difference of two convex functions
 Appl. Math. ENotes
"... We present a scheme to minimize a difference of two convex functions by solving a variational problem. The proposed scheme uses a proximal regularization step (see [8]) to construct a translated fixed point iteration. It can be seen as a descent scheme which takes into consideration the convex prope ..."
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Cited by 2 (0 self)
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We present a scheme to minimize a difference of two convex functions by solving a variational problem. The proposed scheme uses a proximal regularization step (see [8]) to construct a translated fixed point iteration. It can be seen as a descent scheme which takes into consideration the convex
CONTRACTION OF THE PROXIMAL MAP AND GENERALIZED CONVEXITY OF THE MOREAU–YOSIDA REGULARIZATION IN THE 2WASSERSTEIN METRIC
"... msp vol. 1 no. 1 2013 ..."
unknown title
, 2012
"... Contraction of the proximal map and generalized convexity of the MoreauYosida regularization in the 2Wasserstein metric ..."
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Contraction of the proximal map and generalized convexity of the MoreauYosida regularization in the 2Wasserstein metric
Sufficient optimality conditions for the MoreauYosidatype regularization concept applied to the semilinear elliptic optmimal control problems with pointwise state constraints
, 2010
"... We develop sufficient optimality conditions for a MoreauYosida regularized optimal control problem governed by a semilinear elliptic PDE with pointwise constraints on the state and the control. We make use of the equivalence of a setting of MoreauYosida regularization to a special setting of the v ..."
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Cited by 2 (0 self)
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We develop sufficient optimality conditions for a MoreauYosida regularized optimal control problem governed by a semilinear elliptic PDE with pointwise constraints on the state and the control. We make use of the equivalence of a setting of MoreauYosida regularization to a special setting
Results 1  10
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445