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  1. Journal of Optimization Theory and Applications
  2. Journal of Optimization Theory and Applications : Volume 145
  3. Journal of Optimization Theory and Applications : Volume 145, Issue 1, April 2010
  4. Characterizations of r-Convex Functions
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Journal of Optimization Theory and Applications : Volume 173
Journal of Optimization Theory and Applications : Volume 172
Journal of Optimization Theory and Applications : Volume 171
Journal of Optimization Theory and Applications : Volume 170
Journal of Optimization Theory and Applications : Volume 169
Journal of Optimization Theory and Applications : Volume 168
Journal of Optimization Theory and Applications : Volume 167
Journal of Optimization Theory and Applications : Volume 166
Journal of Optimization Theory and Applications : Volume 165
Journal of Optimization Theory and Applications : Volume 164
Journal of Optimization Theory and Applications : Volume 163
Journal of Optimization Theory and Applications : Volume 162
Journal of Optimization Theory and Applications : Volume 161
Journal of Optimization Theory and Applications : Volume 160
Journal of Optimization Theory and Applications : Volume 159
Journal of Optimization Theory and Applications : Volume 158
Journal of Optimization Theory and Applications : Volume 157
Journal of Optimization Theory and Applications : Volume 156
Journal of Optimization Theory and Applications : Volume 155
Journal of Optimization Theory and Applications : Volume 154
Journal of Optimization Theory and Applications : Volume 153
Journal of Optimization Theory and Applications : Volume 152
Journal of Optimization Theory and Applications : Volume 151
Journal of Optimization Theory and Applications : Volume 150
Journal of Optimization Theory and Applications : Volume 149
Journal of Optimization Theory and Applications : Volume 148
Journal of Optimization Theory and Applications : Volume 147
Journal of Optimization Theory and Applications : Volume 146
Journal of Optimization Theory and Applications : Volume 145
Journal of Optimization Theory and Applications : Volume 145, Issue 3, June 2010
Journal of Optimization Theory and Applications : Volume 145, Issue 2, May 2010
Journal of Optimization Theory and Applications : Volume 145, Issue 1, April 2010
Nonsmooth Vector Optimization Problems and Minty Vector Variational Inequalities
Tracking Dirichlet Data in L $^{2}$ is an Ill-Posed Problem
Robust Transferable Sets of Linear Transferring Strategies
Estimates of Variation with Respect to a Set and Applications to Optimization Problems
On the Perpetual Collision-Free RHC of Fleets of Vehicles
Dynamic Game Model of Endogenous Growth with Consumption Externalities
Oligopoly with Hyperbolic Demand: A Differential Game Approach
Piecewise-Linear Approximations of Multidimensional Functions
Coerciveness Property for Conical Nonsmooth Functionals
Global Optimality Conditions for Some Classes of Optimization Problems
Characterizations of r-Convex Functions
Lagrange Multipliers for ε-Pareto Solutions in Vector Optimization with Nonsolid Cones in Banach Spaces
Journal of Optimization Theory and Applications : Volume 144
Journal of Optimization Theory and Applications : Volume 143
Journal of Optimization Theory and Applications : Volume 142
Journal of Optimization Theory and Applications : Volume 141
Journal of Optimization Theory and Applications : Volume 140
Journal of Optimization Theory and Applications : Volume 139
Journal of Optimization Theory and Applications : Volume 138
Journal of Optimization Theory and Applications : Volume 137
Journal of Optimization Theory and Applications : Volume 136
Journal of Optimization Theory and Applications : Volume 135
Journal of Optimization Theory and Applications : Volume 134
Journal of Optimization Theory and Applications : Volume 133
Journal of Optimization Theory and Applications : Volume 132
Journal of Optimization Theory and Applications : Volume 131
Journal of Optimization Theory and Applications : Volume 130
Journal of Optimization Theory and Applications : Volume 129
Journal of Optimization Theory and Applications : Volume 128
Journal of Optimization Theory and Applications : Volume 127
Journal of Optimization Theory and Applications : Volume 126
Journal of Optimization Theory and Applications : Volume 125
Journal of Optimization Theory and Applications : Volume 124
Journal of Optimization Theory and Applications : Volume 123
Journal of Optimization Theory and Applications : Volume 122
Journal of Optimization Theory and Applications : Volume 121
Journal of Optimization Theory and Applications : Volume 120
Journal of Optimization Theory and Applications : Volume 119
Journal of Optimization Theory and Applications : Volume 118
Journal of Optimization Theory and Applications : Volume 117
Journal of Optimization Theory and Applications : Volume 116
Journal of Optimization Theory and Applications : Volume 115
Journal of Optimization Theory and Applications : Volume 114
Journal of Optimization Theory and Applications : Volume 113
Journal of Optimization Theory and Applications : Volume 112
Journal of Optimization Theory and Applications : Volume 111
Journal of Optimization Theory and Applications : Volume 110
Journal of Optimization Theory and Applications : Volume 109
Journal of Optimization Theory and Applications : Volume 108
Journal of Optimization Theory and Applications : Volume 107
Journal of Optimization Theory and Applications : Volume 106
Journal of Optimization Theory and Applications : Volume 105
Journal of Optimization Theory and Applications : Volume 104
Journal of Optimization Theory and Applications : Volume 103
Journal of Optimization Theory and Applications : Volume 102
Journal of Optimization Theory and Applications : Volume 101
Journal of Optimization Theory and Applications : Volume 100
Journal of Optimization Theory and Applications : Volume 99
Journal of Optimization Theory and Applications : Volume 98
Journal of Optimization Theory and Applications : Volume 97
Journal of Optimization Theory and Applications : Volume 96
Journal of Optimization Theory and Applications : Volume 95
Journal of Optimization Theory and Applications : Volume 94
Journal of Optimization Theory and Applications : Volume 93
Journal of Optimization Theory and Applications : Volume 92

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Characterizations of r-Convex Functions

Content Provider SpringerLink
Author Zhao, Y. X. Wang, S. Y. Coladas Uria, L.
Copyright Year 2009
Abstract This paper discusses some properties of r-convexity and its relations with some other types of convexity. A characterization of convex functions in terms of r-convexity is given without assuming differentiability. The concept of strict r-convexity is introduced. For a twice continuously differentiable function f, it is shown that the strict r-convexity of f is equivalent to a certain condition on ∇ $^{2}$ f. Further, it is shown that this condition is satisfied by quasiconvex functions satisfying a less stringent condition.
Starting Page 186
Ending Page 195
Page Count 10
File Format PDF
ISSN 00223239
Journal Journal of Optimization Theory and Applications
Volume Number 145
Issue Number 1
e-ISSN 15732878
Language English
Publisher Springer US
Publisher Date 2009-10-23
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Strict r-convexity r-convexity Positive-semidefinite matrices Positive-definite matrices Convex functions Quasiconvex functions Operations Research/Decision Theory Engineering Applications of Mathematics Theory of Computation Optimization Calculus of Variations and Optimal Control; Optimization
Content Type Text
Resource Type Article
Subject Applied Mathematics Control and Optimization Management Science and Operations Research
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