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We formulate a novel numerical method suitable for the solution of topology optimization problems in solid mechanics. The most salient feature of the new approach is that the space and time discrete equations of the numerical method can be…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for variational…
Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…
We study Hadamard variation of eigenvalues of Laplacian with respect to general domain perturbations. We show their existence up to the second order rigorously and characterize the derivatives, using associated eigenvalue problems in finite…
We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and…
We develop a methodology for closing duality gap and guaranteeing strong duality in infinite convex optimization. Specifically, we examine two new Lagrangian-type dual formulations involving infinitely many dual variables and infinite sums…
We introduce a new arithmetic invariant for hermitian line bundles on an arithmetic variety. We use this invariant to measure the variation of the volume function with respect to the metric. The main result of this paper is a generalized…
We prove general necessary optimality conditions for delta-nabla isoperimetric problems of the calculus of variations.
We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…
This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…
The paper is devoted to an analysis of optimality conditions for nonsmooth multidimensional problems of the calculus of variations with various types of constraints, such as additional constraints at the boundary and isoperimetric…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
We consider second order elliptic systems of partial differential equations subject to Dirichlet and Neumann boundary conditions. We prove analyticity of the elementary symmetric functions of the eigenvalues, and compute Hadamard-type…
The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. This includes the discrete-time, the quantum, and the…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…