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Regions of stability for ill-posed convex programs

Sanjo Zlobec (1982)

Aplikace matematiky

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

Sanjo Zlobec (1986)

Aplikace matematiky

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.

Reliable computation and local mesh adaptivity in limit analysis

Sysala, Stanislav, Haslinger, Jaroslav, Repin, Sergey (2019)

Programs and Algorithms of Numerical Mathematics

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

Paulo J.S. Silva, Carlos Humes (2007)

RAIRO - Operations Research

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...

Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality

Liana Cioban, Ernö Csetnek (2013)

Open Mathematics

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...

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