Asymptotic behavior of regularizable minimizers of a Ginzburg-Landau functional in higher dimensions.
Asymptotic convergence of the steepest descent method for the exponential penalty in linear programming.
Auxiliary principle for generalized nonlinear variational-like inequalities.
Composite algorithms for minimization over the solutions of equilibrium problems and fixed point problems.
Computing optimal control with a quasilinear parabolic partial differential equation.
Constrained optimization: A general tolerance approach
To overcome the somewhat artificial difficulties in classical optimization theory concerning the existence and stability of minimizers, a new setting of constrained optimization problems (called problems with tolerance) is proposed using given proximity structures to define the neighbourhoods of sets. The infimum and the so-called minimizing filter are then defined by means of level sets created by these neighbourhoods, which also reflects the engineering approach to constrained optimization problems....
Convergence of a Penalty-Finite Element Approximation for an Obstacle Problem.
Convergence of the Lagrange-Newton method for optimal control problems
Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is the shooting method, where information on the structure of the optimal solution is exploited. In each case,...
Convergence theorems on generalized equilibrium problems and fixed point problems with applications.
Coplanar control of a satellite around the earth
We investigate the minimum time transfer of a satellite around the Earth. Using an optimal control model, we study the controllability of the system and propose a geometrical analysis of the optimal command structure. Furthermore, in order to solve the problem numerically, a new parametric technique is introduced for which convergence properties are established.
Coplanar control of a satellite around the Earth
We investigate the minimum time transfer of a satellite around the Earth. Using an optimal control model, we study the controllability of the system and propose a geometrical analysis of the optimal command structure. Furthermore, in order to solve the problem numerically, a new parametric technique is introduced for which convergence properties are established.
Correctness of a constrained control Mayer's problem for a class of singularly perturbed functional-differential systems
Critical points of the Ginzburg-Landau functional on multiply-connected domains.
-gap functions and descent methods for a class of monotone equilibrium problems.
Dykstra's algorithm as the nonlinear extension of Bregman's optimization method.
Embedding variational inequalities and their generalizations into a separation scheme.
Evolutionary variational inequalities and applications in plasticity
An abstract theory of evolutionary variational inequalities and its applications to the traction boundary value problems of elastoplasticity are studied, using the penalty method to prove the existence of a solution.
Exact l penalty function for nonsmooth multiobjective interval-valued problems
Our objective in this article is to explore the idea of an unconstrained problem using the exact l penalty function for the nonsmooth multiobjective interval-valued problem (MIVP) having inequality and equality constraints. First of all, we figure out the KKT-type optimality conditions for the problem (MIVP). Next, we establish the equivalence between the set of weak LU-efficient solutions to the problem (MIVP) and the penalized problem (MIVP) with the exact l penalty function. The utility of...
Existence and multiplicity results for homoclinic orbits of Hamiltonian systems.
Existence of solutions for generalized nonlinear mixed variational-like inequalities in Banach spaces.