Some new properties of the Projection DC decomposition algorithm (we call it Algorithm A) and the Proximal DC decomposition algorithm (we call it Algorithm B) Pham Dinh et al. in Optim Methods Softw, 23(4): 609-629 (2...
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Some new properties of the Projection DC decomposition algorithm (we call it Algorithm A) and the Proximal DC decomposition algorithm (we call it Algorithm B) Pham Dinh et al. in Optim Methods Softw, 23(4): 609-629 (2008) for solving the indefinite quadratic programming problem under linear constraints are proved in this paper. Among other things, we show that DCA sequences generated by Algorithm A converge to a locally unique solution if the initial points are taken from a neighborhood of it, and DCA sequences generated by either Algorithm A or Algorithm B are all bounded if a condition guaranteeing the solution existence of the given problem is satisfied.
This paper describes a method for obtaining a mobile manipulator's motion sequence by indicating a goal-hand pose. The proposed method entails recording various robot motions as a large number of motion sequences ...
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This paper describes a method for obtaining a mobile manipulator's motion sequence by indicating a goal-hand pose. The proposed method entails recording various robot motions as a large number of motion sequences and associated swept volumes (SVs) and then selecting the most appropriate SV for the current situation. In addition, the motion sequences can be altered while the robot is in motion, and the transition motion is generated using sequential quadratic programming, enabling the robot to avoid collisions with obstacles found after it has begun to move. The proposed method's performance is verified by simulation to confirm the appropriate amount of data and the method's superiority.
This note describes a reference governor design for a continuous-time nonlinear system with an additive disturbance. The design is based on predicting the response of the nonlinear system, by the response of a linear ...
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This note describes a reference governor design for a continuous-time nonlinear system with an additive disturbance. The design is based on predicting the response of the nonlinear system, by the response of a linear model with a set-bounded prediction error, where a state-and-input-dependent bound on the prediction error is explicitly characterized using logarithmic norms. The online optimization is reduced to a convex quadratic program with linear inequality constraints. Two numerical examples are reported.
Equality-constrained quadratic programming (QP) has been one of the most basic and typical problems in the Internet of Things domain. In big data scenarios, how to quickly and accurately solve the problem in hardware ...
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Equality-constrained quadratic programming (QP) has been one of the most basic and typical problems in the Internet of Things domain. In big data scenarios, how to quickly and accurately solve the problem in hardware has not been realized. Therefore, in this article, a memristive recurrent neural circuit that can parallel solve the QP problem in real time is proposed. First, a new memristive synaptic array is designed that can simultaneously implement parallel reading and writing. On the basis of this structure, a new neural network circuit based on memristor is designed that can perform large-scale recursive operations by parallel methods. This circuit can solve the equality-constrained QP problem in different situations by using such real-time programmable memristor arrays processing in memory. The PSpice simulation results show that the problem can be solved with 99.8% precision. Based on practical verification, the neural circuit experiment on PCB is presented with 97.34% precision. Moreover, the circuit has good robustness under the interference of weight value. And, it has an advantage in processing time compared with FPGA.
An implementation of the recently proposed semi-monotonic augmented Lagrangian algorithm for solving the large convex bound and equality constrained quadratic programming problems is considered. It is proved that if t...
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An implementation of the recently proposed semi-monotonic augmented Lagrangian algorithm for solving the large convex bound and equality constrained quadratic programming problems is considered. It is proved that if the algorithm is applied to the class of problems with uniformly bounded spectrum of the Hessian matrix, then the algorithm finds an approximate solution at O(1) matrix-vector multiplications. The optimality results are presented that do not depend on conditioning of the matrix which defines the equality constraints. Theory covers also the problems with dependent constraints. Theoretical results are illustrated by numerical experiments.
The aim of this paper is to propose an algorithm, based on the optimal level solutions method, which solves a particular class of box constrained quadratic problems. The objective function is given by the sum of a qua...
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The aim of this paper is to propose an algorithm, based on the optimal level solutions method, which solves a particular class of box constrained quadratic problems. The objective function is given by the sum of a quadratic strictly convex separable function and the square of an affine function multiplied by a real parameter. The convexity and the nonconvexity of the problem can be characterized by means of the value of the real parameter. Within the algorithm, some global optimality conditions are used as stopping criteria, even in the case of a nonconvex objective function. The results of a deep computational test of the algorithm are also provided.
Neural networks are known to be sensitive to adversarial perturbations. To investigate this undesired behavior we consider the problem of computing the distance to the decision boundary (DtDB) from a given sample for ...
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Neural networks are known to be sensitive to adversarial perturbations. To investigate this undesired behavior we consider the problem of computing the distance to the decision boundary (DtDB) from a given sample for a deep neural net classifier. In this work we present a procedure where we solve a convex quadratic programming (QP) task to obtain a lower bound on the DtDB. This bound is used as a robustness certificate of the classifier around a given sample. We show that our approach provides better or competitive results in comparison with a wide range of existing techniques.
A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of n Delta on the proximity of optimal solutions of an Integer Linear programming problem and its standard linear relaxation. In this bo...
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A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of n Delta on the proximity of optimal solutions of an Integer Linear programming problem and its standard linear relaxation. In this bound, n is the number of variables and Delta denotes the maximum of the absolute values of the subdeterminants of the constraint matrix. Hochbaum and Shanthikumar, and Werman and Magagnosc showed that the same upper bound is valid if a more general convex function is minimized, instead of a linear function. No proximity result of this type is known when the objective function is nonconvex. In fact, if we minimize a concave quadratic, no upper bound can be given as a function of n and Delta. Our key observation is that, in this setting, proximity phenomena still occur, but only if we consider also approximate solutions instead of optimal solutions only. In our main result we provide upper bounds on the distance between approximate (resp., optimal) solutions to a Concave Integer quadratic programming problem and optimal (resp., approximate) solutions of its continuous relaxation. Our bounds are functions of n, Delta, and a parameter epsilon that controls the quality of the approximation. Furthermore, we discuss how far from optimal are our proximity bounds.
Radial basis function (RBF) surrogate models have been widely applied in engineering design optimization problems to approximate computationally expensive simulations. Ensemble of radial basis functions (ERBF) using t...
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Radial basis function (RBF) surrogate models have been widely applied in engineering design optimization problems to approximate computationally expensive simulations. Ensemble of radial basis functions (ERBF) using the weighted sum of stand-alone RBFs improves the approximation performance. To achieve a good trade-off between the accuracy and efficiency of the modelling process, this article presents a novel efficient ERBF method to determine the weights through solving a quadratic programming subproblem, denoted ERBF-QP. Several numerical benchmark functions are utilized to test the performance of the proposed ERBF-QP method. The results show that ERBF-QP can significantly improve the modelling efficiency compared with several existing ERBF methods. Moreover, ERBF-QP also provides satisfactory performance in terms of approximation accuracy. Finally, the ERBF-QP method is applied to a satellite multidisciplinary design optimization problem to illustrate its practicality and effectiveness for real-world engineering applications.
作者：
Ruiz Galan, M.Univ Granada
ETS Ingn Edificac Dept Appl Math C Severo Ochoa S-N E-18071 Granada Spain
In this paper we are concerned with a Gordan-type theorem involving an arbitrary number of inequality functions. We not only state its validity under a weak convexity assumption on the functions, but also show it is a...
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In this paper we are concerned with a Gordan-type theorem involving an arbitrary number of inequality functions. We not only state its validity under a weak convexity assumption on the functions, but also show it is an optimal result. We discuss generalizations of several recent results on nonlinear quadratic optimization, as well as a formula for the Fenchel conjugate of the supremum of a family of functions, in order to illustrate the applicability of that theorem of the alternative.
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