Sequential quadratic programming methods for parametric nonlinear optimization

Kungurtsev, Vyacheslav; Diehl, Moritz

doi:10.1007/s10589-014-9696-2

Cited by 26 publications

(31 citation statements)

References 30 publications

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“…In some situations, it is possible to guarantee that both E and D are zero, i.e., no convexification is needed. If the problem (6.1) is a convex program then it can be shown that the matrix B ν is positive definite with H = H (see Kungurtsev [37]). Similarly, the elements of H corresponding to fixed variables need not be modified because the corresponding elements of d are always zero.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…This method is clearly impractical for any serious implementation. The discussion of more efficient methods that compute the modified matrix during the solution of the QP subproblem are beyond the scope of this paper (see Kungurtsev [37]). We recognize that other definitions of H are possible, including a positive-definite quasi-Newton approximations based on the BFGS update (see, e.g., [21,42]).…”

Section: Numerical Resultsmentioning

confidence: 99%

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A Globally Convergent Stabilized SQP Method

Gill

Robinson

2013

SIAM J. Optim.

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Sequential quadratic programming (SQP) methods are a popular class of methods for nonlinearly constrained optimization. They are particularly effective for solving a sequence of related problems, such as those arising in mixedinteger nonlinear programming and the optimization of functions subject to differential equation constraints.Recently, there has been considerable interest in the formulation of stabilized SQP methods, which are specifically designed to handle degenerate optimization problems. Existing stabilized SQP methods are essentially local, in the sense that both the formulation and analysis focus on the properties of the methods in a neighborhood of a solution. A new SQP method is proposed that has favorable global convergence properties yet, under suitable assumptions, is equivalent to a variant of the conventional stabilized SQP method in the neighborhood of a solution. The method combines a primal-dual generalized augmented Lagrangian function with a flexible line search to obtain a sequence of improving estimates of the solution. The method incorporates a convexification algorithm that allows the use of exact second-derivatives to define a convex quadratic programming (QP) subproblem without requiring that the Hessian of the Lagrangian be positive definite in the neighborhood of a solution. This gives the potential for fast convergence in the neighborhood of a solution. Additional benefits of the method are that each QP subproblem is regularized and the QP subproblem always has a known feasible point. Numerical experiments are presented for a subset of the problems from the CUTEr test collection.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

A Globally Convergent Stabilized SQP Method

Gill

Robinson

2013

SIAM J. Optim.

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“…We applied the path-following ideas developed in Jäschke et al [24] and Kungurtsev and Diehl [28] to a large-scale process containing a reactor, a distillation column and a recycle stream. Compared with single-step updates based on solving a linear system of equations as proposed by [10], our path-following approach requires somewhat more computational effort.…”

Section: Discussionmentioning

confidence: 99%

“…Note that regardless of the inertia of the Lagrangian Hessian, if the SSOSC holds, it is positive definite on the null-space of the equality constraints, and thus, the QP defined is convex with an easily obtainable finite global minimizer. In [28], it is noted that as the solution to this QP is the directional derivative of the primal-dual solution of the NLP, it is a predictor step, a tangential first-order estimate of the change in the solution subject to a change in the parameter. We refer to the QP (10) as a pure-predictor.…”

Section: Proof See [26] (Sections 51 and 52) And [27] (Propositionmentioning

confidence: 99%

“…However, it is not quite the same, as we enforce the strongly-active constraints as equality constraints in the QP. As explained in [28], this particular QP tries to estimate how the NLP solution changes as the parameter does in the predictor component and refines the estimate, in more closely satisfying the KKT conditions at the new parameter, as a corrector.…”

Section: Path-following Based On Sensitivity Propertiesmentioning

confidence: 99%

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Sensitivity-Based Economic NMPC with a Path-Following Approach

2017

Self Cite

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Abstract:We present a sensitivity-based predictor-corrector path-following algorithm for fast nonlinear model predictive control (NMPC) and demonstrate it on a large case study with an economic cost function. The path-following method is applied within the advanced-step NMPC framework to obtain fast and accurate approximate solutions of the NMPC problem. In our approach, we solve a sequence of quadratic programs to trace the optimal NMPC solution along a parameter change. A distinguishing feature of the path-following algorithm in this paper is that the strongly-active inequality constraints are included as equality constraints in the quadratic programs, while the weakly-active constraints are left as inequalities. This leads to close tracking of the optimal solution. The approach is applied to an economic NMPC case study consisting of a process with a reactor, a distillation column and a recycler. We compare the path-following NMPC solution with an ideal NMPC solution, which is obtained by solving the full nonlinear programming problem. Our simulations show that the proposed algorithm effectively traces the exact solution.

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Recursive quadratic programming for constrained nonlinear optimization of session throughput in multiple‐flow network topologies

Mehta

2020

Engineering Reports

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In this article, we propose and formulate a single‐objective nonlinearly constrained programming problem with delay and capacity constraints. Specifically, we consider the utility resource allocation with the goal of maximizing the throughput amongst the multiple heterogeneous sessions in the network. Several numerical experiments for multiple topologies exhibit the performance and global convergence process of the proposed iterative algorithm. These network topologies are considered with distinct source‐destination communication sessions to emphasize the traffic flow analysis and optimal rate allocation vectors. For this, we employ recursive quadratic programming method and Lagrangian multiplier approach to solve the proposed optimization problem. The presented numerical results are obtained using Octave simulation tool. The results obtained from implementation of numerical simulation demonstrate the robustness and convergence performance of the proposed optimization scheme to optimal solution within finite number of iterations. Finally, we employ various global measures of fairness including the entropy‐based index, G's fairness index, linear product‐based fairness index, and Bossaer's fairness index to assess the performance of the proposed resource allocation scheme.

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Sequential quadratic programming methods for parametric nonlinear optimization

Cited by 26 publications

References 30 publications

A Globally Convergent Stabilized SQP Method

A Globally Convergent Stabilized SQP Method

Sensitivity-Based Economic NMPC with a Path-Following Approach

Recursive quadratic programming for constrained nonlinear optimization of session throughput in multiple‐flow network topologies

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