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Nonlinear Analysis, ISSN 0362-546X, 11/2013, Volume 92, pp. 96 - 107
...ε-duality gap statements for optimization problems consisting of minimizing the sum of a function with the precomposition of a cone-increasing function to a vector function... 
Conjugate functions | Fenchel–Lagrange dual | Constraint qualifications | [formula omitted]-duality gap | Fenchel-Lagrange dual | ε-duality gap | MATHEMATICS | INFINITE-DIMENSIONAL SPACES | MATHEMATICS, APPLIED | REGULARITY CONDITIONS | CONSTRAINT QUALIFICATION | epsilon-duality gap | FENCHEL-LAGRANGE DUALITY | CONJUGATE DUALITY | CONVEX-FUNCTIONS
Journal Article
Neurocomputing, ISSN 0925-2312, 11/2014, Volume 144, pp. 537 - 545
<. p≤2. Leveraging on the theory of Legendre-Fenchel duality, we derive a variational quadratic upper bound of non-differentiable non-convex Lp-norm... 
Feature selection | P-Norm | Support vector machine | Legendre-Fenchel duality | SUPPORT VECTOR MACHINES | p-Norm | SPARSE SIGNALS | BRIDGE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | MINIMIZATION | MODELS | ESTIMATORS | LASSO | VARIABLES | Data mining | Algorithms | Machine learning
Journal Article
Set-valued and variational analysis, ISSN 1877-0541, 2012, Volume 21, Issue 2, pp. 177 - 189
.... This motivates us to present, in this paper, a duality framework for a family of parametric convex optimization problems... 
Geometry | Strong duality | 90C31 | Parametric convex optimization | Uncertain conical convex programs | 90C46 | 90C25 | Analysis | Mathematics | Conjugate duality | Best approximations | MATHEMATICS, APPLIED | PROGRAMS | FENCHEL DUALITY | Family
Journal Article
ANALYSIS AND APPLICATIONS, ISSN 0219-5305, 01/2020, Volume 18, Issue 1, pp. 149 - 183
.... Using the Fenchet-Roclatfellar duality theory, we give an explicit formulation of the dual problem as well as of the related optimality conditions... 
MATHEMATICS | MATHEMATICS, APPLIED | BOUNDS | BANACH-SPACES | Support vector regression | RISK | tensors | Fenchel-Rockatfellar duality | reproducing kernel Banach spaces | REGULARIZATION | regularized empirical risk
Journal Article
Journal of computational and applied mathematics, ISSN 0377-0427, 2016, Volume 292, pp. 150 - 173
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 01/2012, Volume 22, Issue 1
... tensor field, or the strain tensor field, is the unknown. The objective of this paper is to put these three different formulations of the same problem in a new perspective, by means of Legendre-Fenchel duality theory... 
Linearized elasticity | constrained quadratic optimization | Lagrangians | Legendre-Fenchel transform | duality | intrinsic elasticity | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | KORNS INEQUALITY | EQUATIONS | SHELLS | MIXED FINITE-ELEMENTS
Journal Article
Set-Valued and Variational Analysis, ISSN 1877-0533, 6/2016, Volume 24, Issue 2, pp. 253 - 275
.... The results are based on a duality result for increasing set-valued functions. 
Geometry | Quasiconvexity | Dual representation | Analysis | Mathematics | Set-valued functions | Increasing functions | 49N15 | Fenchel-Moreau | 46A20 | MATHEMATICS, APPLIED
Journal Article
Positivity : an international journal devoted to the theory and applications of positivity in analysis, ISSN 1572-9281, 2013, Volume 18, Issue 1, pp. 9 - 28
Journal Article
SIAM journal on optimization, ISSN 1095-7189, 2011, Volume 21, Issue 4, pp. 1230 - 1250
...SIAM J. OPTIM. c Vol. 21, No. 4, pp. 12301250 A MONOTONE + SKEW SPLITTING MODEL FOR COMPOSITE MONOTONE INCLUSIONS IN DUALITY LUIS M. BRICE NO-ARIAS AND PATRICK... 
Monotone inclusion | Minimization algorithm | Convex optimization | Composite operator | Operator splitting | Decomposition | Duality | Fenchel-Rockafellar duality | Monotone operator | Forward-backward-forward algorithm | Mathematics | Optimization and Control
Journal Article
Journal Article
Journal of Convex Analysis, ISSN 0944-6532, 2013, Volume 20, Issue 2, pp. 377 - 394
In this paper, we examine the duality gap between the robust counterpart of a primal uncertain convex optimization problem and the optimistic counterpart of its uncertain Lagrangian dual and identify... 
Convex optimization under uncertainty | Robust optimization | Robust convex programming | Zero duality gap | MATHEMATICS | convex optimization under uncertainty | robust optimization | CONSTRAINT QUALIFICATIONS | zero duality gap | OPTIMIZATION | FENCHEL DUALITY | OPTIMALITY
Journal Article
Optimization, ISSN 0233-1934, 09/2016, Volume 65, Issue 9, pp. 1675 - 1691
... optimization one defined on a separated locally convex topological space. Conditions guaranteeing strong duality for primal problems which are perturbed by continuous... 
Evenly convex function | generalized convex conjugation | Lagrange and Fenchel dual problems | 52A20 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 90C25 | SYSTEMS | 26B25 | CONVOLUTION | Convex analysis | Optimization | Construction | Functionals | Convexity | Conjugation | Perturbation | Topology
Journal Article
by Fang, D.H and Li, C and Ng, K.F
Nonlinear Analysis, ISSN 0362-546X, 2010, Volume 73, Issue 5, pp. 1143 - 1159
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 12/2010, Volume 147, Issue 3, pp. 473 - 482
Journal Article
SIAM journal on optimization, ISSN 1095-7189, 2019, Volume 29, Issue 3, pp. 1819 - 1843
.... Regularity conditions of closedness type for zero duality gap and stability (strong duality) of these problems are established in a general framework... 
MATHEMATICS, APPLIED | summable family of functions | SERIES | regularity condition | CONJUGATE | zero duality gap | EXTENSION | CONVEX-FUNCTIONS | FENCHEL DUALITY | stability
Journal Article
Positivity : an international journal devoted to the theory and applications of positivity in analysis, ISSN 1572-9281, 2010, Volume 15, Issue 3, pp. 527 - 536
Journal Article
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