Search results for " optimization."
showing 10 items of 2333 documents
Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions
2009
Fixed domain methods have well-known advantages in the solution of variable domain problems including inverse interface problems. This paper examines two new control approaches to optimal design problems governed by general elliptic boundary value problems with Dirichlet boundary conditions. Numerical experiments are also included peerReviewed
Regularity of sets under a reformulation in a product space of reduced dimension
2023
Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility problems defined by finitely many sets, some other require the use of a product space reformulation to construct equivalent problems with two sets. In this work we analyze how some regularity properties are preserved under a reformulation in a product space of reduced dimension. This allows us to establish local linear convergence of parallel projection methods which are constructed through this reformulation.
Monge Problem on infinite dimensional Hilbert space endowed with suitable Gaussian measure
2014
In this paper we solve the Monge problem on infinite dimensional Hilbert space endowed with a suitable Gaussian measure, that satisfies the Lebesgue differentiation theorem.
A globally convergent and locally quadratically convergent modified B-semismooth Newton method for $\ell_1$-penalized minimization
2015
We consider the efficient minimization of a nonlinear, strictly convex functional with $\ell_1$-penalty term. Such minimization problems appear in a wide range of applications like Tikhonov regularization of (non)linear inverse problems with sparsity constraints. In (2015 Inverse Problems (31) 025005), a globalized Bouligand-semismooth Newton method was presented for $\ell_1$-Tikhonov regularization of linear inverse problems. Nevertheless, a technical assumption on the accumulation point of the sequence of iterates was necessary to prove global convergence. Here, we generalize this method to general nonlinear problems and present a modified semismooth Newton method for which global converg…
On optimal control of free boundary problems of obstacle type
2018
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed domain. The discretized optimal control problem is a non-smooth and non-convex mathematical programing problem. The performance of the standard BFGS quasi-Newton method and the BFGS method with the inexact line search are tested.
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications
2020
This work is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuska-Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular, …
A combinatorial algorithm for the optimization of refraction seismics data inversion
1993
Abstract The problem of data inversion in refraction seismics can be split in two parts: data first must be preprocessed in order to determine the travel-time curve; this essentially is a geometrical problem, complicated, however, by its pattern recognition aspects. Once the geometrical problem is solved, the second part, the inversion proper, is straightforward, as the soil layering model can be calculated according to well-known algorithms. The more difficult part of the problem is the former, which implies a type of pattern recognition; because of this type of difficulty, the geometrical part of the problem usually is committed to the skill of a human operator. This paper describes an al…
Energy-Efficient Resource Allocation and User Scheduling for Collaborative Mobile Clouds With Hybrid Receivers
2016
In this paper, we study the resource allocation and user scheduling algorithm for minimizing the energy cost of data transmission in the context of OFDMA collaborative mobile cloud (CMC) with simultaneous wireless information and power transfer (SWIPT) receivers. The CMC, which consists of several collaborating MTs offers one potential solution for downlink con- tent distribution and for the energy consumption reduction at the terminal side. Meanwhile, as RF signal can carry both informa- tion and energy simultaneously, the induced SWIPT has gained much attention for energy efficiency design of mobile nodes. Previous work on the design of CMC system mainly focused on the cloud formulation o…
Joint Power Allocation and Link Selection for Multi-Carrier Buffer Aided Relay Network
2019
In this paper, we present a joint power allocation and adaptive link selection protocol for an orthogonal frequency division multiplexing (OFDM)-based network consists of one source node i.e., base station (BS), one destination node i.e., (MU) and a buffer aided decode and forward (DF) relay node. Our objective is to maximize the average throughput of the system via power loading over different subcarriers at source and relay nodes. A separate power budget is assumed at each transmitting node to make the system more practical. In order to form our solution more tractable, a decomposition framework is implemented to solve the mixed integer optimization problem. Further, less complex suboptim…
Energy Efficient Sink Placement in Wireless Sensor Networks by Brain Storm Optimization Algorithm
2018
Wireless sensor networks represent one of the most promising technologies whose use has significantly increased in the past years. They are used in various applications such as health care monitoring, surveillance and monitoring in agriculture, industrial monitoring, habitat and underwater monitoring, etc. Deployment of the wireless sensor networks introduces number of hard optimization problems. Placement of the elements such as sensors, gateways, sinks and base stations, depend on different conditions and constraints such as signal propagation, distance, energy preservation, reliability. In this paper, we propose a method based on brain storm optimization algorithm for placing multiple si…