Related papers: A duality principle and related computational meth…
This article develops a duality principle for a semi-linear model in micro-magnetism. The results are obtained through standard tools of convex analysis and the Legendre transform concept. We emphasize the dual variational formulation…
Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur…
Economic dispatch problem for a networked power system has been considered. The objective is to minimize the total generation cost while meeting the overall supply-demand balance and generation capacity. In particular, a more practical…
We prove a strong duality result for a linear programming problem which has the interpretation of being a discretised optimal Skorokhod embedding problem, and we recover this continuous time problem as a limit of the discrete problems. With…
In this note we explore duality in reverse convex optimization with reverse convex inequality constraints. While we are examining the special case of a finite index set of the inequality constraints, we are primarily interested in the…
We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
In this work we analytically solve an optimal retirement problem, in which the agent optimally allocates the risky investment, consumption and leisure rate to maximise a gain function characterised by a power utility function of consumption…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of…
The application of modern topology optimization techniques to single physics systems has seen great advances in the last three decades. However, the application of these tools to sophisticated multiphysics systems such as fluid-structure…
Gauge functions significantly generalize the notion of a norm, and gauge optimization, as defined by Freund (1987}, seeks the element of a convex set that is minimal with respect to a gauge function. This conceptually simple problem can be…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order…
We prove existence and uniqueness for solutions to equilibrium problems for free-standing, traction-free, non homogeneous crystals in the presence of plastic slips. Moreover we prove that this class of problems is closed under G-convergence…
An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared…
A problem of the erroneous duality gap caused by the presence of symmetries is solved in this paper utilizing point group theory. The optimization problems are first divided into two classes based on their predisposition to suffer from this…