scholarly journals On subspace properties of the quadratically constrained quadratic program

2017 ◽  
Vol 13 (4) ◽  
pp. 1625-1640
Author(s):  
Xin Zhao ◽  
◽  
Jinyan Fan
Keyword(s):  
Quadratic Program ◽  
Quadratically Constrained Quadratic Program ◽  
Quadratically Constrained

A quadratic programming model for the optimization of off-gas networks in integrated steelworks

2019 ◽  
Vol 107 (5) ◽  
pp. 502 ◽  
Author(s):  
Alessandro Maddaloni ◽  
Ruben Matino ◽  
Ismael Matino ◽  
Stefano Dettori ◽  
Antonella Zaccara ◽  
...  
Keyword(s):  
Programming Model ◽  
Steel Production ◽  
Minimum Cost ◽  
Quadratic Program ◽  
Gas Network ◽  
Gas Networks ◽  
Process Gas ◽  
Quadratically Constrained Quadratic Program ◽  
User Friendly ◽  
Quadratically Constrained

The European steel industry is constantly promoting developments, which can increase efficiency and lower the environmental impact of the steel production processes. In particular, a strong focus refers to the minimization of the energy consumption. This paper presents part of the work of the research project entitled “Optimization of the management of the process gas network within the integrated steelworks” (GASNET), which aims at developing a decision support system supporting energy managers and other concerned technical personnel in the implementation of an optimized off-gases management and exploitation considering environmental and economic objectives. A mathematical model of the network as a capacitated digraph with costs on arcs is proposed and an optimization problem is formulated. The objective of the optimization consists in minimizing the wastes of process gases and maximizing the incomes. Several production constraints need to be accounted. In particular, different types of gases are mixing in the same network. The constraints that model the mixing make the problem computationally difficult: it is a non-convex quadratically constrained quadratic program (QCQP). Two formulations of the problem are presented: the first one is a minimum cost flow problem, which is a linear program and is thus computationally fast to solve, but suitable only for a single gas network. The second formulation is a quadratically constrained quadratic program, which is slower, but covers more general cases, such as the ones, which are characterized by the interaction among multiple gas networks. A user-friendly graphical interface has been developed and tests over existing plant networks are performed and analyzed.

Scalable Optimization Methods for Incorporating Spatiotemporal Fractionation into Intensity-Modulated Radiotherapy Planning

2021 ◽  
Author(s):  
Ali Adibi ◽  
Ehsan Salari
Keyword(s):  
Quadratic Programming ◽  
Large Scale ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Radiotherapy Planning ◽  
Quadratic Program ◽  
Clinical Cancer ◽  
Therapeutic Gain ◽  
Solution Methods ◽  
Quadratically Constrained

It has been recently shown that an additional therapeutic gain may be achieved if a radiotherapy plan is altered over the treatment course using a new treatment paradigm referred to in the literature as spatiotemporal fractionation. Because of the nonconvex and large-scale nature of the corresponding treatment plan optimization problem, the extent of the potential therapeutic gain that may be achieved from spatiotemporal fractionation has been investigated using stylized cancer cases to circumvent the arising computational challenges. This research aims at developing scalable optimization methods to obtain high-quality spatiotemporally fractionated plans with optimality bounds for clinical cancer cases. In particular, the treatment-planning problem is formulated as a quadratically constrained quadratic program and is solved to local optimality using a constraint-generation approach, in which each subproblem is solved using sequential linear/quadratic programming methods. To obtain optimality bounds, cutting-plane and column-generation methods are combined to solve the Lagrangian relaxation of the formulation. The performance of the developed methods are tested on deidentified clinical liver and prostate cancer cases. Results show that the proposed method is capable of achieving local-optimal spatiotemporally fractionated plans with an optimality gap of around 10%–12% for cancer cases tested in this study. Summary of Contribution: The design of spatiotemporally fractionated radiotherapy plans for clinical cancer cases gives rise to a class of nonconvex and large-scale quadratically constrained quadratic programming (QCQP) problems, the solution of which requires the development of efficient models and solution methods. To address the computational challenges posed by the large-scale and nonconvex nature of the problem, we employ large-scale optimization techniques to develop scalable solution methods that find local-optimal solutions along with optimality bounds. We test the performance of the proposed methods on deidentified clinical cancer cases. The proposed methods in this study can, in principle, be applied to solve other QCQP formulations, which commonly arise in several application domains, including graph theory, power systems, and signal processing.

scholarly journals Design of Robust Pulses to Insufficient Synchronization for OFDM/OQAM Systems in Doubly Dispersive Channels

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Yu Zhao ◽  
Xihong Chen ◽  
Lunsheng Xue ◽  
Qun Zhang
Keyword(s):  
Orthogonal Frequency Division Multiplexing ◽  
Pulse Shaping ◽  
Optimization Problem ◽  
Carrier Frequency Offset ◽  
Hermite Functions ◽  
Quadratic Program ◽  
Frequency Division ◽  
Timing Offset ◽  
Dispersive Channels ◽  
Quadratically Constrained

This paper presents a pulse shaping method robust to insufficient synchronization in orthogonal frequency division multiplexing with offset quadrature amplitude modulation (OFDM/OQAM) systems over doubly dispersive (DD) channels. The proposed pulse is designed as a linear combination of several well localized Hermite functions. The coefficients optimization problem is modeled as a nonconvex constrained fractional programming problem based on the signal-to-interference ratio (SIR) maximization criterion. An efficient iterative algorithm is applied to simplify the problem to a series of quadratically constrained quadratic program (QCQP) problems which can be solved by semidefinite relaxation (SDR) method. Simulation results show that the proposed pulse is superior to traditional pulses with respect to SIR performance over DD channels in the presence of carrier frequency offset (CFO) and timing offset (TO).

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