Semi-infinite programming problems
Separation by hyperplanes in finite-dimensional vector spaces over Archimedean ordered fields.
Slice convergence : stabilité et optimisation dans les espaces non réflexifs
Il est démontré par Mentagui [ESAIM : COCV 9 (2003) 297-315] que, dans le cas des espaces de Banach généraux, la convergence d’Attouch-Wets est stable par une classe d’opérations classiques de l’analyse convexe, lorsque les limites des suites d’ensembles et de fonctions satisfont certaines conditions de qualification naturelles. Ceci tombe en défaut avec la slice convergence. Dans cet article, nous établissons des conditions de qualification uniformes assurant la stabilité de la slice convergence...
Slice convergence: stabilité et optimisation dans les espaces non réflexifs
Il est démontré par Mentagui [ESAIM: COCV9 (2003) 297-315] que, dans le cas des espaces de Banach généraux, la convergence d'Attouch-Wets est stable par une classe d'opérations classiques de l'analyse convexe, lorsque les limites des suites d'ensembles et de fonctions satisfont certaines conditions de qualification naturelles. Ceci tombe en défaut avec la slice convergence. Dans cet article, nous établissons des conditions de qualification uniformes assurant la stabilité de la slice convergence...
Sliding subspace design based on linear matrix inequalities
In this work, an alternative for sliding surface design based on linear and bilinear matrix inequalities is proposed. The methodology applies for reduced and integral sliding mode control, both continuous- and discrete-time; it takes advantage of the Finsler's lemma to provide a greater degree of freedom than existing approaches for sliding subspace design. The sliding surfaces thus constructed are systematically found via convex optimization techniques, which are efficiently implemented in commercially...
Smoothing a polyhedral convex function via cumulant transformation and homogenization
Given a polyhedral convex function g: ℝⁿ → ℝ ∪ +∞, it is always possible to construct a family which converges pointwise to g and such that each gₜ: ℝⁿ → ℝ is convex and infinitely often differentiable. The construction of such a family involves the concept of cumulant transformation and a standard homogenization procedure.
Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems
There has been much interest in studying symmetric cone complementarity problems. In this paper, we study the circular cone complementarity problem (denoted by CCCP) which is a type of nonsymmetric cone complementarity problem. We first construct two smoothing functions for the CCCP and show that they are all coercive and strong semismooth. Then we propose a smoothing algorithm to solve the CCCP. The proposed algorithm generates an infinite sequence such that the value of the merit function converges...
Solving convex program via Lagrangian decomposition
We consider general convex large-scale optimization problems in finite dimensions. Under usual assumptions concerning the structure of the constraint functions, the considered problems are suitable for decomposition approaches. Lagrangian-dual problems are formulated and solved by applying a well-known cutting-plane method of level-type. The proposed method is capable to handle infinite function values. Therefore it is no longer necessary to demand the feasible set with respect to the non-dualized...
Some aspects of fractional programming
Some remarks on subdifferentiability of convex functions.
Sphärische Abbildung konvexer abgeschlossener Mengen in und ihre charakteristischen Eigenschaften
Nachdem der Begriff des sphärischen Bildes der Menge und der Begriff von sphärisch äquivalenten Mengen eingeführt wurde, werden verschiedene Zusammenhänge zwischen der Menge und ihrem sphärischen Bild untersucht und zwar unter verschiedenen Voraussetzung über (z. B. ihre Beschränkheit, Unbeschränkheit, strenge Konvexität). Die bewiesene Tatsache, dass die Menge und ihre -Umgebung sphärisch äquivalent sind, kann - sowie andere Ergebnisse der Arbeit - in der Theorie der konvexen parametrischen...
Stabilité de L'épi-convergence en Dimension Finie
Stability and duality in convex minimization problems
Strong-weak Stackelberg Problems in Finite Dimensional Spaces
We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation...
Sur des méthodes d'optimisation par relaxation
Sur la dualité en optimisation vectorielle convexe
Sur la méthode de Wolfe et la méthode de Dantzig en programmation quadratique convexe
Sur la minimisation de fonctionnelles convexes par pénalisation
Sur les fonctions presque affines
The Continuous Linearization Method of the Fourth Order