A Sequential Linear Programming Algorithm for Continuous and Mixed-Integer Nonconvex Quadratic Programming

Bentobache, Mohand; Telli, Mohamed; Mokhtari, Abdelkader

doi:10.1007/978-3-030-21803-4_3

Cited by 2 publications

(3 citation statements)

References 12 publications

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“…The obtained numerical simulation results on four convex and non-convex linearquadratic optimal control problems arising in mechanics show that the new direct method converges fastly to the optimal value of the quality criterion found by the analytical method. In a future work, we will apply the algorithm developed in [4] to efficiently solve the non-convex quadratic programming problems obtained by the discretization methods presented in this work. Furthermore, we will adapt the proposed algorithm for solving linear-quadratic optimal control problems, where the matrices of the linear dynamical system depend on the time.…”

Section: Discussionmentioning

confidence: 99%

“…However, ASM can give local solutions which are not global for other non-convex test-problems not considered in this work. So in order to find a good approximate global optimal solution for the non-convex quadratic programming problems of the form (13), we can use the sequential linear programming algorithm developed in [4] for solving non-convex quadratic programs.…”

Section: Examplementioning

confidence: 99%

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Direct method to solve linear-quadratic optimal control problems

Aliane¹,

Bentobache²,

Moussouni³

et al. 2021

NACO

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In this work, we have proposed a new approach for solving the linear-quadratic optimal control problem, where the quality criterion is a quadratic function, which can be convex or non-convex. In this approach, we transform the continuous optimal control problem into a quadratic optimization problem using the Cauchy discretization technique, then we solve it with the active-set method. In order to study the efficiency and the accuracy of the proposed approach, we developed an implementation with MATLAB, and we performed numerical experiments on several convex and non-convex linearquadratic optimal control problems. The obtained simulation results show that our method is more accurate and more efficient than the method using the classical Euler discretization technique. Furthermore, it was shown that our method fastly converges to the optimal control of the continuous problem found analytically using the Pontryagin's maximum principle.

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Section: Discussionmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Direct method to solve linear-quadratic optimal control problems

Aliane¹,

Bentobache²,

Moussouni³

et al. 2021

NACO

Self Cite

View full text Add to dashboard Cite

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“…• Note that this version of SLPA is an improved version of that proposed in [4]. Moreover, in [7,11] the denominators of the numbers α j can be equal to zero when u j = x (see Formula ( 5)).…”

Section: The Successive Linear Programming Algorithm For Continuous Nonconvex Qpmentioning

confidence: 99%

New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

2021

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In this work, we propose a new approach called "Successive Linear Programming Algorithm (SLPA)" for finding an approximate global minimizer of general nonconvex quadratic programs. This algorithm can be initialized by any extreme point of the convex polyhedron of the feasible domain. Furthermore, we generalize the simplex algorithm for finding a local minimizer of concave quadratic programs written in standard form. We prove a new necessary and sufficient condition for local optimality, then we describe the Revised Primal Simplex Algorithm (RPSA). Finally, we propose a hybrid local-global algorithm called "SLPLEX", which combines RPSA with SLPA for solving general concave quadratic programs. In order to compare the proposed algorithms to the branch-and-bound algorithm of CPLEX12.8 and the branch-and-cut algorithm of Quadproga, we develop an implementation with MATLAB and we present numerical experiments on 139 nonconvex quadratic test problems. KeywordsNonconvex quadratic programming • Concave quadratic programming • Successive linear programming • Simplex algorithm • Extreme point • Local minimizer • Global minimizer • Approximate global minimizer • Numerical experiments Mathematics Subject Classification 90C20 • 90C26 • 90C59 B Mohand Bentobache

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A Sequential Linear Programming Algorithm for Continuous and Mixed-Integer Nonconvex Quadratic Programming

Cited by 2 publications

References 12 publications

Direct method to solve linear-quadratic optimal control problems

Direct method to solve linear-quadratic optimal control problems

New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

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