quadratic programming‎

In this paper‎,‏‎ we use the least squares method to solve LR fuzzy interval systems by transforming an interval fuzzy number into two triangular fuzzy numbers. Then, ‎w‎e reduce the distance between the two obtained triangular fuzzy numbers to solve the fuzzy ‎LR‎ interval linear system. Essentially, we convert an LR fuzzy interval linear system into a triangular fuzzy linear system and subsequently solve it using the least squares method introduced ‎in [17, 18].

A concurrent learning (CL) adaptive control is proposed for a class of nonlinear systems in the presence of dead-zone input nonlinearity to guarantee the exponential convergence of the tracking and the parameter estimation errors. The proposed method enriches and encompasses the conventional filtering-based CL by proposing robust and optimal terms. The optimal term is designed by solving a suitable quadratic programming optimization problem based on control Lyapunov function theory which also meets the need for prescribed control bounds. A suitable robust term is proposed to tackle the presence of the dead-zone input nonlinearity. Recent methods of adaptive CL tune the control parameters using trial and error, which is a tedious task. In this paper, by some analysis and proposing two nonlinear optimization problems, the values of the control parameters are derived. The nonlinear optimization problems are solved using the time-varying iteration particle swarm optimization algorithm. The simulation results indicate the effectiveness of the proposed method.

We propose logarithmic-barrier decomposition-based interior-point algorithms for solving two-stage stochastic quadratically constrained convex quadratic programming problems in a Hilbert space. We prove the polynomial complexity of the proposed algorithms, and show that this complexity is independent on the choice of the Hilbert space, and hence it coincides with the best-known complexity estimates in the finite-dimensional case. We also apply our results on a concrete example from the stochastic control theory.

This paper presents a capable recurrent neural network, the so-called µRNN for solving a class of non-convex quadratic programming problems‎. ‎Based on the optimality conditions we construct a new recurrent neural network (µRNN)‎, ‎which has a simple structure and its capability is preserved‎. ‎The proposed neural network model is stable in the sense of Lyapunov and converges to the exact optimal solution of the original problem‎. ‎In a particular case‎, ‎the optimality conditions of the problem become necessary and sufficient‎. ‎Numerical experiments and comparisons with some existing algorithms are presented to illustrate the theoretical results and show the efficiency of the proposed network.

This paper studies the quadratic programming problem subject to asystem of bipolar fuzzy relation equations with the max-productcomposition. A characterization of structure of its feasible domain is presented using the lower and upper bound vector on its solution set. A sufficient condition is proposed which under the condition, a component of one of its optimal solutions is the corresponding component of either the lower or upper bound vector. Some sufficient conditions are suggested to reveal one of its optimal solutions without resolution of the problem. Furthermore, some sufficient conditions are then given to determine some components from one of its optimal solutions. Based on these conditions, we can simplify the problem and reduce its dimensions. The simplified problem can be reformulated to an 0-1 mixed integer programming problem. Other unknown variables can be found by solving the current problem.

This manuscript extends the CSW model to stochastic inputs and outputs. Next, the stochastic CSW model is transformed into a nonlinear model, and then, the deterministic model is transformed into a quadratic programming model. Finally, the concept presented in this article is demonstrated through a numerical example involving a number of Iranian banks.

‎In this paper‎, ‎the linear support vector regression approach is proposed for solving the regression problem with interval data‎, ‎which is called interval support vector regression(ISVR)‎. ‎The ISVR approach is equivalent to solving a linear constrained quadratic programming problem (QPP) with an interval cost coefficient in which the value of the objective function is in an interval‎. ‎Instead of solving an interval QPP‎, ‎we solve two QPPs and prove that the cost values of these two problems are the lower bound and the upper bound of the target value of the interval QPP‎. ‎We show these two mentioned QPPs are equivalent to two support vector regression problems which the first problem applies the lower bound of data and the second problem considers the upper bound of the data‎. ‎to obtain the regression function‎. ‎Some experiments are made to demonstrate the performance of our method compared with the known algorithms on several artificial‎, ‎benchmark and real practical datasets‎.‎‎‎

Support Vector Regression (SVR) solves regression problems based on the concept of Support Vector Machine (SVM). In this paper, a new model of SVR with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. Using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadratic optimization problem. The proposed method is illustrated by several simulated data and real data sets for both models (linearand nonlinear) with probabilistic constraints.

This paper proposes a quadratic programming method (QPM) for ranking alternatives based on multiplicative preference relations (MPRs) and fuzzy preference relations (FPRs). The proposed QPM can be used for deriving a ranking from either a MPR or a FPR, or a group of MPRs, or a group of FPRs, or their mixtures. The proposed approach is tested and examined with two numerical examples, and comparative analyses with the existing methods are provided to show the effectiveness and advantages of the QPM.

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we show that the worst-case iteration bound for our IPM is O(6(m)3m(m)Ψm(m)01θlognμ0ε), where m>4.