Qualitative analysis of basic notions in parametric convex programming. II. Parameters in the objective function
Qualitative analysis of basic notions in parametric convex programming. I. Parameters in the constraints
Quasi-Newton type of diagonal updating for the L-BFGS method.
Quelques notes et résultats nouveaux sur le problème d'équilibre d'un oligopole
Regions of stability for ill-posed convex programs
Regions of stability are chunks of the space of parameters in which the optimal solution and the optimal value depend continuously on the data. In these regions the problem of solving an arbitrary convex program is a continuous process and Tihonov's regularization is possible. This paper introduces a new region we furnisch formulas for the marginal value. The importance of the regions of stability is demostrated on multicriteria decision making problems and in calculating the minimal index set...
Regions of stability for ill-posed convex programs: An addendum
The marginal value formula in convex optimization holds in a more restrictive region of stability than that recently claimed in the literature. This is due to the fact that there are regions of stability where the Lagrangian multiplier function is discontinuous even for linear models.
Relación entre conos de direcciones decrecientes y conos de direcciones de descenso.
Sea f: N → R una función convexa y sea x ∈ Ni, donde N es un convexo en un espacio vectorial real. Se demuestra que, si Df<(x) es no vacío, entonces Df<(x) es el interior algebraico de Df≤(x).
Relatively inexact proximal point algorithm and linear convergence analysis.
Reliable computation and local mesh adaptivity in limit analysis
The contribution is devoted to computations of the limit load for a perfectly plastic model with the von Mises yield criterion. The limit factor of a prescribed load is defined by a specific variational problem, the so-called limit analysis problem. This problem is solved in terms of deformation fields by a penalization, the finite element and the semismooth Newton methods. From the numerical solution, we derive a guaranteed upper bound of the limit factor. To achieve more accurate results, a local...
Rescaled proximal methods for linearly constrained convex problems
We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps even for Linear Programming. This is achieved by using an error criterion that bounds the subgradient...
Résolution de problèmes d'optimisation dynamique par programmation dynamique marginaliste
Reverse convex problems: an approach based on optimality conditions.
Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality
Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka...
Riemannian convexity.
Riemannian convexity in programming. II.
Saddle point criteria for second order -approximated vector optimization problems
The purpose of this paper is to apply second order -approximation method introduced to optimization theory by Antczak [2] to obtain a new second order -saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order -saddle point and the second order -Lagrange function are defined for the second order -approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution of the...
Schwach verkoppelte Ungleichungssysteme und konvexe Spline-Interpolation.
Second order convexity and a modified objective function method in mathematical programming
Selection strategies in projection methods for convex minimization problems
We propose new projection method for nonsmooth convex minimization problems. We present some method of subgradient selection, which is based on the so called residual selection model and is a generalization of the so called obtuse cone model. We also present numerical results for some test problems and compare these results with some other convex nonsmooth minimization methods. The numerical results show that the presented selection strategies ensure long steps and lead to an essential acceleration...
Semidefinite programming and combinatorial optimization.