In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local ...In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.展开更多
On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear pro...On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.展开更多
In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to...In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to its growth term increasing linearly. Some new analysis tools were developed which can be used to deal with complexity "analysis of the algorithms which use analogous strategy in [5] to design the search directions for the Newton system. The complexity bounds for the algorithms with large- and small-update methodswere obtained, namely,O(qn^(p+q/q(P+1)log n/ε and O(q^2√n)log n/ε,respectlvely.展开更多
In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization (CQO) based on a kernel function is presented. The proposed function has some properties that are easy for checking. These ...In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization (CQO) based on a kernel function is presented. The proposed function has some properties that are easy for checking. These properties enable us to improve the polynomial complexity bound of a large-update interior-point method (IPM) to O(√n log nlog n/e), which is the currently best known polynomial complexity bound for the algorithm with the large-update method. Numerical tests were conducted to investigate the behavior of the algorithm with different parameters p, q and θ, where p is the growth degree parameter, q is the barrier degree of the kernel function and θ is the barrier update parameter.展开更多
In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming (LP) problems. The algorithms are based on a few kernel functions, including both serf-regular functio...In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming (LP) problems. The algorithms are based on a few kernel functions, including both serf-regular functions and non-serf-regular ones. The dynamic step size is compared with fixed step size for the algorithms in inner iteration of Newton step. Numerical tests show that the algorithms with dynaraic step size are more efficient than those with fixed step size.展开更多
We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and...We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.展开更多
To preserve the edges and details of the image,a new variational model for wavelet domain inpainting was proposed which contained a non-convex regularizer. The non-convex regularizer can utilize the local information ...To preserve the edges and details of the image,a new variational model for wavelet domain inpainting was proposed which contained a non-convex regularizer. The non-convex regularizer can utilize the local information of image and perform better than those usual convex ones. In addition, to solve the non-convex minimization problem,an iterative reweighted method and a primaldual method were designed. The numerical experiments show that the new model not only gets better visual effects but also obtains higher signal to noise ratio than the recent method.展开更多
In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex n...In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.展开更多
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle for t...The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.展开更多
Aiming at obtaining high power density of surface-mounted and interior permanent magnet synchronous motor(SIPMSM),it is important to accurately calculate the temperature field distribution of SIPMSM,and a magnetic-the...Aiming at obtaining high power density of surface-mounted and interior permanent magnet synchronous motor(SIPMSM),it is important to accurately calculate the temperature field distribution of SIPMSM,and a magnetic-thermal coupling method is proposed.The magnetic-thermal coupling mechanism is analyzed.The thermal network model and finite element model are built by this method,respectively.The effects of power frequency on iron losses and temperature fields are analyzed by the magnetic-thermal coupling finite element model under the condition of rated load,and the relationship between the load and temperature field is researched under the condition of the synchronous speed.In addition,the equivalent thermal network model is used to verify the magnetic-thermal coupling method.Then the temperatures of various nodes are obtained.The results show that there are advantages in both computational efficiency and accuracy for the proposed coupling method,which can be applied to other permanent magnet motors with complex structures.展开更多
It is well known that the incorrect results will be given using either the electric or magnetic field integral equation to calculate the radar cross section (RCS) of a closed body at the interior resonance. In this pa...It is well known that the incorrect results will be given using either the electric or magnetic field integral equation to calculate the radar cross section (RCS) of a closed body at the interior resonance. In this paper, an effective iterative technique is used to correct the calculated surface current density from the electric field integral equation. The radar cross section is computed for an infinite conducting circular cylinder at the interior resonance, and the obtained results are in good agreement with the analytical results. The backscattering cross section of an infinite triangular cylinder in the vicinity of a resonant frequency is also calculated. It is shown that the presence method is efficient and accurate.展开更多
Under the environment of electric power market, economic dispatch (ED) problem should consider network constraints, unit ramp rates, besides the basic constraints. For this problem, it is important to establish the ef...Under the environment of electric power market, economic dispatch (ED) problem should consider network constraints, unit ramp rates, besides the basic constraints. For this problem, it is important to establish the effective model and algorithm. This paper examines the decoupled conditions that affect the solution optimality to this problem. It proposes an effective model and solution method. Based on the look-ahead technique, it finds the number of time intervals to guarantee the solution optimality. Next, an efficient technique for finding the optimal solution via the interior point methods is described. Test cases, which include dispatching six units over 5 time intervals on the IEEE 30 test system with line flows and ramp constraints are presented. Results indicate that the computational effort as measured by iteration counts or execution time varies only modestly with the problem size.展开更多
In this paper,we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method.Under suitable conditions,a constructive proof is given to prove the existence o...In this paper,we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method.Under suitable conditions,a constructive proof is given to prove the existence of fixed points,which can lead to an implementable globally convergent algorithm.展开更多
Many numerical methods,such as tensor network approaches including density matrix renormalization group calculations,have been developed to calculate the extreme/ground states of quantum many-body systems.However,litt...Many numerical methods,such as tensor network approaches including density matrix renormalization group calculations,have been developed to calculate the extreme/ground states of quantum many-body systems.However,little attention has been paid to the central states,which are exponentially close to each other in terms of system size.We propose a delta-Davidson(DELDAV)method to efficiently find such interior(including the central)states in many-spin systems.The DELDAV method utilizes a delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem.Numerical experiments on Ising spin chain and spin glass shards show the correctness,efficiency,and robustness of the proposed method in finding the interior states as well as the ground states.The sought interior states may be employed to identify many-body localization phase,quantum chaos,and extremely long-time dynamical structure.展开更多
In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids....In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.展开更多
The finite-dimensional variational inequality problem (VIP) has been studied extensively in the literature because of its successful applications in many fields such as economics, transportation, regional science and ...The finite-dimensional variational inequality problem (VIP) has been studied extensively in the literature because of its successful applications in many fields such as economics, transportation, regional science and operations research. Barker and Pang[1] have given an excellent survey of theories, methods and applications of VIPs.展开更多
A new higher-order accurate space-time discontinuous Galerkin(DG)method using the interior penalty flux and discontinuous basis functions,both in space and in time,is pre-sented and fully analyzed for the second-order...A new higher-order accurate space-time discontinuous Galerkin(DG)method using the interior penalty flux and discontinuous basis functions,both in space and in time,is pre-sented and fully analyzed for the second-order scalar wave equation.Special attention is given to the definition of the numerical fluxes since they are crucial for the stability and accuracy of the space-time DG method.The theoretical analysis shows that the DG discre-tization is stable and converges in a DG-norm on general unstructured and locally refined meshes,including local refinement in time.The space-time interior penalty DG discre-tization does not have a CFL-type restriction for stability.Optimal order of accuracy is obtained in the DG-norm if the mesh size h and the time stepΔt satisfy h≅CΔt,with C a positive constant.The optimal order of accuracy of the space-time DG discretization in the DG-norm is confirmed by calculations on several model problems.These calculations also show that for pth-order tensor product basis functions the convergence rate in the L∞and L2-norms is order p+1 for polynomial orders p=1 and p=3 and order p for polynomial order p=2.展开更多
This work focuses on the application of the reconstruction method of differentiated backprojection (DBP)-projection onto convex sets (POCS) in the interior problem.First,we present the definition of the interior p...This work focuses on the application of the reconstruction method of differentiated backprojection (DBP)-projection onto convex sets (POCS) in the interior problem.First,we present the definition of the interior problem and real truncated Hilbert transform,and then outline the implementation steps of DBP-POCS.After that,we introduce the middle-part known condition for region of interest (ROI) accurate reconstruction and the unique condition of the interior problem,and verify the uniqueness and stability of the interior problem accurate reconstruction through numerical experiments,and then compare the results for the interior problem in reconstruction images using filtered backprojection (FBP).In addition,the authors also design the application models of ROI reconstruction and make an initial attempt to the application of DBP-POCS method in the interior problem.展开更多
Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicit...Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicity and quick progress in the early iterations. In this work, to accelerate the convergence of the interior point method, few iterations of this generalized algorithm are applied to the Mehrotra’s heuristic, which determines the starting point for the interior point method in the PCx software. Computational experiments in a set of linear programming problems have shown that this approach reduces the total number of iterations and the running time for many of them, including large-scale ones.展开更多
文摘In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.
文摘On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.
文摘In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to its growth term increasing linearly. Some new analysis tools were developed which can be used to deal with complexity "analysis of the algorithms which use analogous strategy in [5] to design the search directions for the Newton system. The complexity bounds for the algorithms with large- and small-update methodswere obtained, namely,O(qn^(p+q/q(P+1)log n/ε and O(q^2√n)log n/ε,respectlvely.
基金the Foundation of Scientific Research for Selecting and Cultivating Young Excellent University Teachers in Shanghai (Grant No.06XPYQ52)the Shanghai Pujiang Program (Grant No.06PJ14039)
文摘In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization (CQO) based on a kernel function is presented. The proposed function has some properties that are easy for checking. These properties enable us to improve the polynomial complexity bound of a large-update interior-point method (IPM) to O(√n log nlog n/e), which is the currently best known polynomial complexity bound for the algorithm with the large-update method. Numerical tests were conducted to investigate the behavior of the algorithm with different parameters p, q and θ, where p is the growth degree parameter, q is the barrier degree of the kernel function and θ is the barrier update parameter.
基金Project supported by Dutch Organization for Scientific Research(Grant No .613 .000 .010)
文摘In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming (LP) problems. The algorithms are based on a few kernel functions, including both serf-regular functions and non-serf-regular ones. The dynamic step size is compared with fixed step size for the algorithms in inner iteration of Newton step. Numerical tests show that the algorithms with dynaraic step size are more efficient than those with fixed step size.
基金supported by the National Natural Science Foundation of China(11571132,12301542)the Natural Science Foundation of Hubei(2022CFB725)the Natural Science Foundation of Yichang(A23-2-027)。
文摘We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.
基金National Natural Science Foundations of China(Nos.61301229,61101208)Doctoral Research Funds of Henan University of Science and Technology,China(Nos.09001708,09001751)
文摘To preserve the edges and details of the image,a new variational model for wavelet domain inpainting was proposed which contained a non-convex regularizer. The non-convex regularizer can utilize the local information of image and perform better than those usual convex ones. In addition, to solve the non-convex minimization problem,an iterative reweighted method and a primaldual method were designed. The numerical experiments show that the new model not only gets better visual effects but also obtains higher signal to noise ratio than the recent method.
文摘In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.
基金Project supported by the National Natural Science Foundation of China (Grant No.10872163)the Natural Science Foundation of Education Department of Shaanxi Province (Grant No.08JK394)
文摘The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.
基金This work was supported by Natural Science Foundation of China(Item number:51777060,U1361109)Natural Science Foundation of Henan province(Item number:162300410117)the he innovative research team plan of Henan Polytechnic University(Item number:T2015-2).
文摘Aiming at obtaining high power density of surface-mounted and interior permanent magnet synchronous motor(SIPMSM),it is important to accurately calculate the temperature field distribution of SIPMSM,and a magnetic-thermal coupling method is proposed.The magnetic-thermal coupling mechanism is analyzed.The thermal network model and finite element model are built by this method,respectively.The effects of power frequency on iron losses and temperature fields are analyzed by the magnetic-thermal coupling finite element model under the condition of rated load,and the relationship between the load and temperature field is researched under the condition of the synchronous speed.In addition,the equivalent thermal network model is used to verify the magnetic-thermal coupling method.Then the temperatures of various nodes are obtained.The results show that there are advantages in both computational efficiency and accuracy for the proposed coupling method,which can be applied to other permanent magnet motors with complex structures.
基金This project was supported by the Foundation of MOE of China (No. 00179).
文摘It is well known that the incorrect results will be given using either the electric or magnetic field integral equation to calculate the radar cross section (RCS) of a closed body at the interior resonance. In this paper, an effective iterative technique is used to correct the calculated surface current density from the electric field integral equation. The radar cross section is computed for an infinite conducting circular cylinder at the interior resonance, and the obtained results are in good agreement with the analytical results. The backscattering cross section of an infinite triangular cylinder in the vicinity of a resonant frequency is also calculated. It is shown that the presence method is efficient and accurate.
文摘Under the environment of electric power market, economic dispatch (ED) problem should consider network constraints, unit ramp rates, besides the basic constraints. For this problem, it is important to establish the effective model and algorithm. This paper examines the decoupled conditions that affect the solution optimality to this problem. It proposes an effective model and solution method. Based on the look-ahead technique, it finds the number of time intervals to guarantee the solution optimality. Next, an efficient technique for finding the optimal solution via the interior point methods is described. Test cases, which include dispatching six units over 5 time intervals on the IEEE 30 test system with line flows and ramp constraints are presented. Results indicate that the computational effort as measured by iteration counts or execution time varies only modestly with the problem size.
基金Supported by the NNSF of China(11026079)Supported by the Youth Backbone Teacher Foundation of Henan Province(173)
文摘In this paper,we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method.Under suitable conditions,a constructive proof is given to prove the existence of fixed points,which can lead to an implementable globally convergent algorithm.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91836101,U1930201,and 11574239).
文摘Many numerical methods,such as tensor network approaches including density matrix renormalization group calculations,have been developed to calculate the extreme/ground states of quantum many-body systems.However,little attention has been paid to the central states,which are exponentially close to each other in terms of system size.We propose a delta-Davidson(DELDAV)method to efficiently find such interior(including the central)states in many-spin systems.The DELDAV method utilizes a delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem.Numerical experiments on Ising spin chain and spin glass shards show the correctness,efficiency,and robustness of the proposed method in finding the interior states as well as the ground states.The sought interior states may be employed to identify many-body localization phase,quantum chaos,and extremely long-time dynamical structure.
文摘In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.
基金The NNSF (10071031) of China and National 973 Project.
文摘The finite-dimensional variational inequality problem (VIP) has been studied extensively in the literature because of its successful applications in many fields such as economics, transportation, regional science and operations research. Barker and Pang[1] have given an excellent survey of theories, methods and applications of VIPs.
文摘A new higher-order accurate space-time discontinuous Galerkin(DG)method using the interior penalty flux and discontinuous basis functions,both in space and in time,is pre-sented and fully analyzed for the second-order scalar wave equation.Special attention is given to the definition of the numerical fluxes since they are crucial for the stability and accuracy of the space-time DG method.The theoretical analysis shows that the DG discre-tization is stable and converges in a DG-norm on general unstructured and locally refined meshes,including local refinement in time.The space-time interior penalty DG discre-tization does not have a CFL-type restriction for stability.Optimal order of accuracy is obtained in the DG-norm if the mesh size h and the time stepΔt satisfy h≅CΔt,with C a positive constant.The optimal order of accuracy of the space-time DG discretization in the DG-norm is confirmed by calculations on several model problems.These calculations also show that for pth-order tensor product basis functions the convergence rate in the L∞and L2-norms is order p+1 for polynomial orders p=1 and p=3 and order p for polynomial order p=2.
基金supported by the National Natural Science Foundation of China (Grant No.60872116)
文摘This work focuses on the application of the reconstruction method of differentiated backprojection (DBP)-projection onto convex sets (POCS) in the interior problem.First,we present the definition of the interior problem and real truncated Hilbert transform,and then outline the implementation steps of DBP-POCS.After that,we introduce the middle-part known condition for region of interest (ROI) accurate reconstruction and the unique condition of the interior problem,and verify the uniqueness and stability of the interior problem accurate reconstruction through numerical experiments,and then compare the results for the interior problem in reconstruction images using filtered backprojection (FBP).In addition,the authors also design the application models of ROI reconstruction and make an initial attempt to the application of DBP-POCS method in the interior problem.
文摘Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicity and quick progress in the early iterations. In this work, to accelerate the convergence of the interior point method, few iterations of this generalized algorithm are applied to the Mehrotra’s heuristic, which determines the starting point for the interior point method in the PCx software. Computational experiments in a set of linear programming problems have shown that this approach reduces the total number of iterations and the running time for many of them, including large-scale ones.