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.

Introduction Over the past decade, applications in dynamic simulation have increased signicantly in the process industries. These are driven by strong competitive markets faced by operating companies along with tighter specications on process performance and regulatory limits. Moreover, the developmentofpowerful commercial modeling tools for dynamic simulation, such as ASPEN Custom # ####### ########################## #### ############### ################### 1 Modeler and gProms, has led to their introduction in industry alongside their widely used steady state counterparts. Dynamic optimization is the natural extension of these dynamic simulation tools because it automates many of the decisions required for engineering studies. Applications of dynamic simulation can be classied into o-line and on-line tasks. O-line tasks include: # Design to avoid undesirable transients for chemical process

This paper introduces a method and tool-support for the automatic analysis and verification of hybrid and embedded control systems, whose continuous dynamics are often modelled using MATLAB/Simulink. The method is based upon converting system models into the uniform input language of our efficient multi-domain constraint solving library, ABSOLVER, which is then used for subsequent analysis. Basically, ABSOLVER is an extensible SMT-solver which addresses mixed Boolean and (nonlinear) arithmetic constraint problems as they appear in the design of hybrid control systems. It allows the integration and semantic connection of various domain specific solvers via a logical circuit, such that almost arbitrary multi-domain constraint problems can be formulated and solved. Its design has been tailored for extensibility, and thus facilitates the reuse of expert knowledge, in that the most appropriate solver for a given task can be integrated and used. As such the only constraint over the problem domain is the capability of the employed solvers. Our approach to systems verification has been validated in an industrial case study using the model of a car’s steering control system. However, additional benchmarks show that other hard instances of problems could also be solved by ABSOLVER in respectable time, and that for some instances, ABSOLVER’s approach was the only means of solving a problem at all. 1

Abstract This paper considers strategies for selecting the barrier parameter at every iterationof an interior-point method for nonlinear programming. Numerical experiments suggest that adaptive choices, such as Mehrotra's probing procedure, outperform static strate-gies that hold the barrier parameter fixed until a barrier optimality test is satisfied. A new adaptive strategy is proposed based on the minimization of a quality function. Thepaper also proposes a globalization framework that ensures the convergence of adaptive interior methods. The barrier update strategies proposed in this paper are applica-ble to a wide class of interior methods and are tested in the two distinct algorithmic frameworks provided by the ipopt and knitro software packages.

We propose a globalization strategy for nonlinear constrained optimization. The method employs a “flexible” penalty function to promote convergence, where during each iteration the penalty parameter can be chosen as any number within a prescribed interval, rather than a fixed value. This increased flexibility in the step acceptance procedure is designed to promote long productive steps for fast convergence. An analysis of the global convergence properties of the approach in the context of a line search Sequential Quadratic Programming method and numerical results for the KNITRO software package are presented.

Introduction Engineering modeling systems form the cornerstone of analysis and design in a broad range of disciplines. In computational mechanics and the analysis of transport systems, a wide variety of PDE modeling systems and products are available. In addition to solving discretized partial dierential equations, most of these also have capabilities for mesh generation, many options for construction of nite element bases and a wide variety of linear iterative solvers and preconditioners. These engineering systems represent dozens of man-years of software development. However, virtually all of them were developed for analysis and not for design optimization. As a result, there remain some interesting challenges in leveraging this software investment in order to adapt these systems for optimization. In principle, such systems require smooth functions and rst (and possibly second) derivatives to be accessed from the modeling equations by the nonlinear programming (NLP) algor

Abstract. We compare six state-of-the-art local optimization solvers with focus on their efficiency when invoked within an interval-based global optimization algorithm. For comparison purposes we design three special performance indicators: a solution check indicator (measuring whether the local minimizers found are good candidates for near-optimal verified feasible points), a function value indicator (measuring the contribution to the progress of the global search), and the running time indicator (estimating the computational cost of the local search within the global search). The solvers are compared on the COCONUT Environment test set consisting of 1307 problems. Our main target is to predict the behavior of the solvers in terms of the three performance indicators on a new problem. For this we introduce a k-nearest neighbor method applied over a feature space consisting of several categorical and numerical features of the optimization problems. The quality and robustness of the prediction is demonstrated by various quality measurements with detailed comparative tests. In particular, we found that on the test set we are able to pick a ‘best ’ solver in 66–89 % of the cases and avoid picking all ‘useless ’ solvers in 95–99 % of the cases (when a useful alternative exists). The resulting automated solver selection method is implemented as an inference engine of the COCONUT Environment.

The main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic optimization problems. We briefly present library classes for the formulation and manipulation of dynamic optimization problems, and give a general survey of solver classes for unconstrained and constrained optimization. We also demonstrate methods of derivative evaluation that we used, in particular automatic differentiation. Further, we briefly formulate and characterize the class of problems solved by our optimization classes. The solution of dynamic optimization problems with general constraints is performed by transformation into structured large-scale nonlinear programming problems and applying methods for nonlinear optimization. Two main algorithms of solvers for constrained dynamic optimization are presented in detail: the sequential quadratic programming (SQP) exploring the multistage structure of the dynamic optimization problem during the solution of a sequence of quadratic subproblems, and the nonlinear interior-point method implemented in a general-purpose large-scale optimizer IPOPT. At the end, we include a typical numerical example of the application of the constrained solvers to a large-scale discrete-time optimal control problem and we use the performance profiles methodology to compare the efficiency and robustness of different solvers or different options of the same solver. In conclusions, we summarize our experience gathered during the library development.

Many recent convergence results obtained for primal-dual interior-point methods for nonlinear programming, use assumptions of the boundedness of generated iterates. In this paper we replace such assumptions by new assumptions on the NLP problem, develop a modification of a primal-dual interior-point method implemented in software package loqo and analyze convergence of the new method from any initial guess. Keywords. Interior-point method, primal-dual, convergence analysis. 1

Abstract not found