We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a co...
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We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IPOPT code, which we demonstrate in a detailed numerical study based on 954 problems from the CUTEr test set. An evaluation is made of several line-search options, and a comparison is provided with two state-of-the-art interior-point codes for nonlinear programming.
In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation...
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In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation, which can aid in solving ill-behaved problems and in warmstarting the algorithm. We present details of our implementation within the LOQO algorithm and provide extensive numerical results on the CUTEr test set and on warmstarting in the context of quadratic, nonlinear, mixed integer nonlinear, and goal programming.
The aim of this paper is to show that the theorem on the global convergence of the Newton interior-point (IP) method presented in Ref. 1 can be proved under weaker assumptions. Indeed, we assume the boundedness of the...
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The aim of this paper is to show that the theorem on the global convergence of the Newton interior-point (IP) method presented in Ref. 1 can be proved under weaker assumptions. Indeed, we assume the boundedness of the sequences of multipliers related to nontrivial constraints, instead of the hypothesis that the gradients of the inequality constraints corresponding to slack variables not bounded away from zero are linearly independent. By numerical examples, we show that, in the implementation of the Newton IP method, loss of boundedness in the iteration sequence of the multipliers detects when the algorithm does not converge from the chosen starting point.
This paper develops a novel nonlinear numerical method to perform shakedown analysis of structures subjected to variable loads by means of nonlinear programming techniques and the displacement-based finite element met...
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This paper develops a novel nonlinear numerical method to perform shakedown analysis of structures subjected to variable loads by means of nonlinear programming techniques and the displacement-based finite element method. The analysis is based on a general yield function which can take the form of most soil yield criteria (e.g. the Mohr-Coulomb or Drucker-Prager criterion). Using an associated flow rule, a general yield criterion can be directly introduced into the kinematic theorem of shakedown analysis without linearization. The plastic dissipation power can then be expressed in terms of the kinematically admissible velocity and a nonlinear formulation is obtained. By means of nonlinear mathematical programming techniques and the finite element method, a numerical model for kinematic shakedown analysis is developed as a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the shakedown load can be calculated. An effective, direct iterative algorithm is then proposed to solve the resulting nonlinear programming problem. The calculation is based on the kinematically admissible velocity with one-step calculation of the elastic stress field. Only a small number of equality constraints are introduced and the computational effort is very modest. The effectiveness and efficiency of the proposed numerical method have been validated by several numerical examples. (c) 2006 Elsevier Ltd. All rights reserved.
In accord with the practical engineering design conditions, a nonlinear programming model is constructed for maximizing the fatigue life of V-belt drive in which some polymorphic uncertainties are incorporated. For a ...
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In accord with the practical engineering design conditions, a nonlinear programming model is constructed for maximizing the fatigue life of V-belt drive in which some polymorphic uncertainties are incorporated. For a given satisfaction level and a confidence level, an equivalent formulation of this uncertain optimization model is obtained where only interval parameters are involved. Based on the concepts of maximal and minimal range inequalities for describing interval inequality, the interval parameter model is decomposed into two standard nonlinear programming problems, and an algorithm, called two-step based sampling algorithm, is developed to find an interval optimal solution for the original problem. Case study is employed to demonstrate the validity and practicability of the constructed model and the algorithm.
We propose a monotone descent active set QP-free method for inequality constrained optimization that ensures the feasibility of all iterates and allows for iterates on the boundary of the feasible set. The study is mo...
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We propose a monotone descent active set QP-free method for inequality constrained optimization that ensures the feasibility of all iterates and allows for iterates on the boundary of the feasible set. The study is motivated by the Facchinei - Fischer - Kanzow active set identification technique for nonlinear programming and variational inequalities [ F. Facchinei, A. Fischer, and C. Kanzow, SIAM J. Optim., 9 ( 1999), pp. 14 - 32]. Distinguishing features of the proposed method compared with existing QP-free methods include lower subproblem costs and a fast convergence rate under milder assumptions. Specifically, four reduced linear systems with a common coefficient matrix involving only constraints in a working set are solved at each iteration. To determine the working set, the method makes use of multipliers from the last iteration, eliminating the need to compute a new estimate, and no additional linear systems are solved to select linearly independent constraint gradients. A new technique is presented to avoid possible ill-conditioned Newton systems caused by dual degeneracy. It is shown that the method converges globally to KKT points under the linear independence constraint qualification (LICQ), and the asymptotic rate of convergence is Q-superlinear under an additional strong second-order sufficient condition (SSOSC) without strict complementarity.
In this paper, we consider a nonlinear programming problem for which the constraint set may be infeasible. We propose an algorithm based on a large family of augmented Lagrangian functions and analyze its global conve...
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In this paper, we consider a nonlinear programming problem for which the constraint set may be infeasible. We propose an algorithm based on a large family of augmented Lagrangian functions and analyze its global convergence properties taking into account the possible infeasibility of the problem. We show that, in a finite number of iterations, the algorithm stops detecting the infeasibility of the problem or finds an approximate feasible/optimal solution with any required precision. We illustrate, by means of numerical experiments, that our algorithm is reliable for different Lagrangian/penalty functions proposed in the literature.
In this paper, a new sequential quadratic programming (SQP) method of feasible directions is proposed and analyzed for nonlinear programming, where a feasible direction of descent can be derived from solving only one ...
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In this paper, a new sequential quadratic programming (SQP) method of feasible directions is proposed and analyzed for nonlinear programming, where a feasible direction of descent can be derived from solving only one QP subproblem. In particular, this method can produce automatically a revised direction with the explicit expression which can avoid Maratos effect without solving QP subproblem. The theoretical analysis shows that global and superlinear convergence can be induced. In the end, numerical experiment is given to illustrate the effectiveness of the method. (C) 2002 Elsevier Inc. All rights reserved.
An attempt is made to model a gas lift allocation problem as a nonlinear optimization form with a wide range of constraints covering deficiencies carried out by past studies. In this article, a rigorous nonlinear prog...
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An attempt is made to model a gas lift allocation problem as a nonlinear optimization form with a wide range of constraints covering deficiencies carried out by past studies. In this article, a rigorous nonlinear programming approach is used to maximize daily cash flow of a group of production wells under gas lift operation. First, an appropriate model is prepared for gas lift performance curve of each well by use of nonlinear logarithmic and polynomial regression. Afterward, a model is constructed and solved for daily cash flow under capacity and pressure constraints. Results show a significant increase in cash flow for an optimized case compared with the current gas allocation plan. Moreover, sensitivity analysis was performed for different variables showing that oil price and compressing cost must be considered in long-term gas lift allocation optimization.
We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qual...
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We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sufficient conditions for their Lagrange multiplier set to be nonempty. MPCCs that have nonempty Lagrange multiplier sets and satisfy the quadratic growth condition can be approached by the elastic mode with a bounded penalty parameter. In this context, the elastic mode transforms MPCC into a nonlinear program with additional variables that has an isolated stationary point and local minimum at the solution of the original problem, which in turn makes it approachable by sequential quadratic programming (SQP) algorithms. One such algorithm is shown to achieve local linear convergence once the problem is relaxed. Under stronger conditions, we also prove superlinear convergence to the solution of an MPCC using an adaptive elastic mode approach for an SQP algorithm recently analyzed in an MPCC context in [R. Fletcher, S. Leyffer, S. Sholtes, and D. Ralph, Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints, Tech. report NA 210, University of Dundee, Dundee, UK, 2002]. Our assumptions are more general since we do not use a critical assumption from that reference. In addition, we show that the elastic parameter update rule will not interfere locally with the superlinear convergence once the penalty parameter is appropriately chosen.
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