Bounds for convex quadratic programming problems and some important applications

The brain-computer interface (BCI) P300 speller analyzes the P300 signals from the brain to achieve direct communication between humans and machines, which can assist patients with severe disabilities to control external machines or robots to complete expected tasks. Therefore, the classification method of P300 signals plays an important role in the development of BCI systems and technologies. In this article, a novel ensemble support vector recurrent neural network (E-SVRNN) framework is proposed and developed to acquire more accurate and efficient electroencephalogram (EEG) signal classification results. First, we construct a support vector machine (SVM) to formulate EEG signals recognizing model. Second, the SVM formulation is transformed into a standard convex quadratic programming (QP) problem. Third, the convex QP problem is solved by combining a varying parameter recurrent neural network (VPRNN) with a penalty function. Experimental results on BCI competition II and BCI competition III datasets demonstrate that the proposed E-SVRNN framework can achieve accuracy rates as high as 100% and 99%, respectively. In addition, the results of comparison experiments verify that the proposed E-SVRNN possesses the best recognition accuracy and information transfer rate (ITR) compared with most of the state-of-the-art algorithms.

This paper proposes a hybrid stochastic-deterministic approach to realize the observer-based active fault diagnosis (AFD) for linear time varying systems. A novel conception called hybrid zonotope-Gaussian dispersity for random variables of systems is introduced to establish an online optimization strategy for AFD. The optimal gain of observer and the optimal input are simultaneously designed at each step by solving a non-convex quadratic fractional programming problem, which is proved to be equivalent to a mixed integer quadratic programming problem. The proposed approach avoids the strict set-separation constraint conditions of traditional offline AFD technology by making full use of the online measured outputs such that the diagnosisability of systems has potential to be further improved. At the end, a quadrotor model is used to verify the effectiveness of our proposed method.

Ranking in quadratic integer programming problems

Multi-parametric programming based algorithms for the global solution of bi-level mixed-integer linear and quadratic programming problems

Redundant robot manipulators are usually applied to various complex scenarios where harmful noise especially periodic calculating noise always exists. In order to avoid the task failure affected by the periodic noise, a circadian rhythms neural network (CRNN) is applied to solve motion planning problems of redundant robot manipulators suffering from the periodic noise. First, in this article, we formulate a tracking problem of redundant manipulators as a convex quadratic programming (QP) problem. Second, the QP problem is converted into a matrix equation. Third, based on the neural dynamic design method, a CRNN model is exploited and developed to solve the matrix equation of the tracking problem. Comparative simulations between the proposed CRNN and the traditional zeroing neural network show that the CRNN has better robustness and performance on solving the end-effector tracking task. Two physical experiments are conducted to further certify the effectiveness, robustness, and practicability of the proposed CRNN.

Demand uncertainty is one critical form of uncertainty which has an adverse effect on Air traffic flow management (ATFM). This is mainly due to the deviation in departure time and aircraft speed from their scheduled values. This may lead to the arrival of aircraft to certain routes at unscheduled times, causing an unexpected demand on those routes. The uncertainty of demand creates several difficulties in air transportation systems, including higher workloads for air traffic controllers, higher delays, travel costs, as well as safety risk. In this study, we propose a robust flight routing and scheduling scheme while considering both departure and speed uncertainty present in the air traffic network. Following robust optimization, we ensure that the capacity violations are eliminated from the system. The ATFM problem is formulated as a Mixed Integer Quadratic Programming (MIQP) problem with the objective of minimizing expected total delay of the system while maintaining required in-trail separation between aircraft even under uncertainty. In addition, we use an optimal flight level assignment method and speed assignment strategy to minimize the system delay and to fully utilize the system capacity. Furthermore, a greedy strategy with parallel computation is presented with the problem decomposed into a set of maximum independent sets to reduce the computational complexity in solving large-scale ATFM problems. With the experimental results, we demonstrate the effectiveness of the model.

The intelligence level of distribution networks keeps improving in recent years. For example, in China, the distribution transformer supervisory terminal unit(TTU), which can intelligently monitor and manage the distribution transformer area, is being widely installed in distribution networks. These TTUs can provide real-time distribution transformer operation data. To increase the value of these data, this paper focuses on the line switch statuses identification technology in distribution networks using TTU measurement data. Firstly, based on the analysis of the TTU measurement data, an optimization equation of which the objective function is the residual error between measurements and estimations is formulated. Secondly, the nonlinear terms in the original optimization equation are eliminated, and it is converted into a mixed integer quadratic programming(MIQP) problem so that it can be solved using the standard method. Moreover, a voltage measurement correction algorithm using the solution of the objective function is proposed. Finally, case studies are conducted to verify the effectiveness of the proposed method.

By using linear constraints on integer variables, logical inference can be incorporated within Model Predictive Control and model based detection problems resulting in mixed integer quadratic or mixed integer linear programming problems. Qualitative knowledge can be used to prioritize control objectives, or to improve performance of detection schemes. This article demonstrates some capabilities of combining logic using integer variables with quantitative models. An extended version is available from: ftp://ftp.ant.ee.ethz.ch/pnb/reports/postscript/ AUT96-15.ps.

In this paper, we show that minimizing the product of path lengths results in minimizing the probability of connection failure between a source and destination given two links have failed in the network. We, therefore, analyze the problem of finding disjoint paths between two nodes with the minimum path length product. We formulate the problem as a mixed integer quadratic programming (MIQP) problem. We develop an iterative heuristic based on k-shortest path approach. We demonstrate through extensive simulations that only a few iterations are sufficient to obtain paths whose path length product is comparable to that of optimal obtained by solving the MIQP.

Receding horizon load restoration for coupled transmission and distribution system considering load-source uncertainty

A simple plant-location model for quantity-setting firms subject to price uncertainty

Model predictive control (MPC) has been considered as one important feed-forward optimal control strategy for ocean wave energy converter (WEC) targeted on power maximization. The capability of MPC to handle system constraints (ex. stroke, velocity, actuator limitations), and the availability to provide optimal solution for linear system provide potential for the implementation of such algorithm in the WEC control. However, currently, only active MPC control has been introduced for single and two-body WECs. Such control strategy may introduce negative power during the optimization process, since the power take-off (PTO) damping has no constraint. In this paper, we proposed a hybrid MPC strategy in limiting both the PTO damping force and PTO damping to avoid negative power generation during cost function minimization (negative power minimization) for the two-body WEC. The problem is formulated into a quadratic programming (QP) problem targeted at power maximization. However, the standard QP problem formulation cannot be directly applied to the semi-active control problem due to the PTO damping constraints. Therefore, the problem is reformulated as a Mixed-integer Quadratic Programming (MIQP) problem, which contains logical switch to select constraint matrices based on the sign of the relative velocity between the buoy and submerged body. The optimal solution is compared with those of the active MPC control strategy and the passive model with the same irregular wave input.

Maximum a posteriori (MAP) inference in Markov random field (MRF) lays the foundation for many computer vision tasks, which can be formulated by a binary quadratic programming (BQP) problem. Compar...

This paper presents a novel halftoning algorithm based on continuous relaxation and gradient-based optimization. By reformulating the original binary quadratic programming (BQP) problem into a differentiable non-convex objective, the proposed method integrates a perceptual loss with a binarization regularizer to guide the optimization toward high-quality binary outputs. Unlike deep learning-based approaches, our method is model-free, memory-efficient, and fully interpretable, enabling fast convergence without complex training or large memory overhead. Experimental results demonstrate that the proposed method outperforms both classical and neural halftoning techniques in terms of image quality and convergence speed. This work provides a practical and scalable solution for highresolution halftone image generation, particularly suitable for industrial and real-time applications under resource constraints.

Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a function with unfavorable properties like multimodality, non-differentiability, and invariability with respect to some transformations. Recently various two-level optimization algorithms for multidimensional scaling with city-block distances have been proposed exploiting piecewise quadratic structure of the least squares objective function with such distances. A problem of combinatorial optimization is tackled at the upper level, and convex quadratic programming problems are tackled at the lower level. In this paper we discuss a new reformulation of the problem where lower level quadratic programming problems seem more suited for two-level optimization.