arXiv subjects

Wim Van Roy

Publications and source records attributed to Wim Van Roy.

5 recordsLinked to original sources

arXiv2026

A Sequential Benders-based Mixed-Integer Quadratic Programming Algorithm and Its Implementation in the CAMINO Toolbox

Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer quadratic programming (MIQP) algorithm to extend this methodology to mixed-integer nonlinear problems (MINLPs), leveraging the efficiency of modern MIQP solvers. The algorithm uses a three-step iterative process. First, the MINLP is linearized around the current iterate. Second, an MIQP is formulated and solved, with its feasible region restricted to a specific area around the linearization point. This region is defined using objective values and derivatives from previous iterations, drawing on concepts from generalized Benders' decomposition. Third, the integer variables from the MIQP solution are fixed, and an NLP involving only the continuous variables is solved. The best solution among all iterates becomes the linearization point for the next iteration. A fallback strategy based on a mixed-integer linear program (MILP) is used when MIQP progress stalls. This guarantees convergence to the global optimal solution for convex MINLPs. For nonconvex problems, the algorithm functions as a heuristic without global optimality guarantees. Numerical experiments show its competitiveness with other MINLP solvers on benchmark problems. In addition, the algorithm was successfully applied to mixed-integer optimal control problems, demonstrating its effectiveness in handling challenging nonlinear equality constraints. The proposed algorithm is publicly available at https://github.com/minlp-toolbox/CAMINO with the name s-b-miqp.

math.OC↗

arXiv2025

Iterative Switching Time Optimization for Mixed-integer Optimal Control Problems

This paper proposes an iterative method to solve Mixed-Integer Optimal Control Problems arising from systems with switched dynamics. The so-called relaxed problem plays a central role within this context. Through a numerical example, it is shown why relying on the relaxed problem can lead the solution astray. As an alternative, an iterative Switching Time Optimization method is proposed. The method consists of two components that iteratively interact: a Switching Time Optimization (STO) problem and a sequence optimization. Each component is explained in detail, and the numerical example is resolved, the results of which shows the efficiency of the proposed algorithm. Finally, the advantages and disadvantages of the method are discussed and future lines of research are sketched.

math.OC↗

arXiv2025

Three-dimensional Optical Reconstruction of colloidal electrokinetics via multiplane imaging

Sorting, filtering, moving and controlling colloidal particles is crucial in many fields, ranging from chemistry to biology and physics. Dielectrophoresis is an outstanding tool for the manipulation of small particles by AC electric fields, due to its high selectivity and the absence of the need for labels. We use a new theoretical-experimental approach to study the dynamics of fluorescently labeled polystyrene nanoparticles of 200 nm under positive and negative dielectrophoresis conditions. Our multiplane widefield microscopy technique combined with single particle tracking offers real-time ($>$ 100 fps) superresolved visualization of colloidal dynamics in three spatial dimensions. This real-time 3D imaging technique allows the reconstruction of superresolved trajectories, enabling the visualisation of local forces with unprecedented detail. To interpret this data, a dedicated multiscale modeling approach was developed, targeting a direct comparison between theory and experiment. In the current model DEP and electro-osmotic forces were considered. Under positive DEP conditions, this resulted in a very good agreement with experiment. Under negative DEP conditions, the agreement is less clear, indicating the importance of other effects. This illustrates the potential of this combined 3D imaging and modeling approach to validate and refine our theoretical understanding of AC field induced colloidal dynamics. This framework is broadly applicable to other complex fluid or microfluidic motion.

cond-mat.soft↗

arXiv2012

Understanding nanoscale temperature gradients in magnetic nanocontacts

We determine the temperature profile in magnetic nanocontacts submitted to the very large current densities that are commonly used for spin-torque oscillator behavior. Experimentally, the quadratic current-induced increase of the resistance through Joule heating is independent of the applied temperature from 6 K to 300 K. The modeling of the experimental rate of the current-induced nucleation of a vortex under the nanocontact, assuming a thermally-activated process, is consistent with a local temperature increase between 150 K and 220 K. Simulations of heat generation and diffusion for the actual tridimensional geometry were conducted. They indicate a temperature-independent efficiency of the heat sinking from the electrodes, combined with a localized heating source arising from a nanocontact resistance that is also essentially temperature-independent. For practical currents, we conclude that the local increase of temperature is typically 160 K and it extends 450 nm about the nanocontact. Our findings imply that taking into account the current-induced heating at the nanoscale is essential for the understanding of magnetization dynamics in nanocontact systems.

cond-mat.mes-hall↗

arXiv2012

Boosting the Figure Of Merit of LSPR-based refractive index sensing by phase-sensitive measurements

Localized surface plasmon resonances possess very interesting properties for a wide variety of sensing applications. In many of the existing applications only the intensity of the reflected or transmitted signals is taken into account, while the phase information is ignored. At the center frequency of a (localized) surface plasmon resonance, the electron cloud makes the transition between in- and out-of-phase oscillation with respect to the incident wave. Here we show that this information can experimentally be extracted by performing phase-sensitive measurements, which result in linewidths that are almost one order of magnitude smaller than those for intensity based measurements. As this phase transition is an intrinsic property of a plasmon resonance, this opens up many possibilities for boosting the figure of merit (FOM) of refractive index sensing by taking into account the phase of the plasmon resonance. We experimentally investigated this for two model systems: randomly distributed gold nanodisks and gold nanorings on top of a continuous gold layer and a dielectric spacer and observed FOM values up to 8.3 and 16.5 for the respective nanoparticles.

physics.optics↗