Related papers: Second-order supporting quadric method for designi…
The current bottleneck of globally solving mixed-integer (non-convex) quadratically constrained problem (MIQCP) is still to construct strong but computationally cheap convex relaxations, especially when dense quadratic functions are…
In this paper, we propose new linearly convergent second-order methods for minimizing convex quartic polynomials. This framework is applied for designing optimization schemes, which can solve general convex problems satisfying a new…
Higher-order perturbations during the ringdown phase are essential for testing gravitational theories. This requires a perturbation framework that extends beyond General Relativity, as well as an appropriate method for reconstructing the…
We consider distributed optimization with smooth convex objective functions defined on an undirected connected graph. Inspired by mirror descent mehod and RLC circuits, we propose a novel distributed mirror descent method. Compared with…
Modeling second-order ($\chi^{(2)}$) nonlinear optical processes remains computationally expensive due to the need to resolve fast field oscillations and simulate wave propagation using methods like the split-step Fourier method (SSFM).…
Stochastic gradient method (SGM) has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SGMs assume that the underlying problem is unconstrained or…
We present an inverse method for transforming a given parallel light emittance to two light distributions at different parallel target planes using two freeform reflectors. The reflectors control both the spatial and directional target…
Achieving quantum-limited motional control of optically trapped particles beyond the sub-micrometer scale is an outstanding problem in levitated optomechanics. A key obstacle is solving the light scattering problem and identifying particle…
In this paper, we propose an efficient joint precoding design method to maximize the weighted sum-rate in wideband intelligent reflecting surface (IRS)-assisted cell-free networks by jointly optimizing the active beamforming of base…
This thesis presents new mathematical algorithms for the numerical solution of a mathematical problem class called \emph{dynamic optimization problems}. These are mathematical optimization problems, i.e., problems in which numbers are…
In this paper, we propose a trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method for solving optimization problems with a stochastic objective and deterministic nonlinear equality and inequality…
In this letter, we consider the fundamental problem of jointly designing the transmit beamformers and the phase-shifts of the intelligent reflecting surface (IRS) / reconfigurable intelligent surface (RIS) to minimize the transmit power,…
The fast growing scale and heterogeneity of current communication networks necessitate the design of distributed cross-layer optimization algorithms. So far, the standard approach of distributed cross-layer design is based on dual…
The Multi-Layer Thin Films Problem is a materials science problem that aims to enhance the reflectance of a metallic substrate by designing multi-layer coatings composed of different dielectric materials and thicknesses. While previous…
Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special…
This paper deals with the highly challenging problem of reconstructing the shape of a refracting object from a single image of its resulting caustic. Due to the ubiquity of transparent refracting objects in everyday life, reconstruction of…
This paper proposes a new large-scale mask-compliant spectral precoder (LS-MSP) for orthogonal frequency division multiplexing systems. In this paper, we first consider a previously proposed mask-compliant spectral precoding scheme that…
We introduce a novel approach to calculating three-dimensional freeform reflectors with a scattering surface. Our method is based on optimal transport and utilizes a Fredholm integral equation to express scattering. By solving this integral…
As a wide class of resource management problems in wireless communications are nonconvex and even NP-hard in many cases, finding globally optimal solutions to these problems is of little practical interest. Towards more pragmatic…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…