CONTENTS
1. Introduction and preliminaries....................................................5
1.1. Introduction............................................................................5
1.2. Organization..........................................................................6
1.3. Prerequisites.........................................................................6
1.4. Introductory examples...........................................................9
2. Elementary properties.............................................................14
2.1. Basic facts...........................................................................14
2.2. Infimal convolution of subadditive functions.........................17
2.3. Semicontinuity, continuity, and exactness............................19
2.4. Two examples......................................................................22
3. The convex case.....................................................................23
3.1. Basic results........................................................................23
3.2. Differential calculus, and first order differentiability..............28
3.3. Formulas on f ▫ g.................................................................31
3.4. Loss of differentiability.........................................................32
4. Continuity of the operation of infimal convolution....................33
4.1. Introduction.........................................................................34
4.2. Epi-convergence.................................................................35
4.3. The Mosco topology and the slice topology.........................36
4.4. The affine topology..............................................................38
4.5. The Attouch-Wets topology.................................................39
5. Regularization.........................................................................41
5.1. Introduction and first results................................................41
5.2. Approximation in Hilbert spaces...........................................47
5.3. Generalized Moreau-Yosida approximation.........................52
References..................................................................................55