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ON COMBINING FEASIBILITY, DESCENT AND SUPERLINEAR CONVERGENCE IN INEQUALITY CONSTRAINED OPTIMIZATION

MATHEMATICAL programming 1993年第2期59卷 261-276页

作者： PANIER, ER TITS, AL UNIV MARYLAND DEPT ELECT ENGNCOLL PKMD 20742 UNIV MARYLAND CTR SYST RESCOLL PKMD 20742

Extension of quasi-Newton techniques from unconstrained to constrained optimization via sequential quadratic programming (SQP) presents several difficulties. Among these are the possible inconsistency, away from the solution, of first order approximations to the constraints, resulting in infeasibility of the quadratic programs;and the task oe selecting a suitable merit function, to induce global convergence. In ths case of inequality constrained optimization, both of these difficulties disappear if the algorithm is forced to generate iterates that all satisfy the constraints, and that yield monotonically decreasing objective function values. (Feasibility of the successive iterates is in fact required in many contexts such as in real-time applications or when the objective function is not well defined outside the feasible set.) It has been recently shown that this can be achieved while preserving local two-step superlinear convergence. In this note, the essential ingredients for an SQP-based method exhibiting the desired properties are highlighted. Correspondingly, a class of such algorithms is described and analyzed. Tests performed with an efficient implementation are discussed.

关键词： CONSTRAINED OPTIMIZATION sequential quadratic programming FEASIBILITY SUPERLINEAR CONVERGENCE

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Maximizing Demineralization during Chemical Leaching of Coal through Optimal Reagent Addition Policy

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CHEMICAL PRODUCT AND PROCESS MODELING 2015年第1期10卷 1-9页

作者： Dash, Pratik S. Prasad, D. N. Sriramoju, Santosh K. Lingam, R. K. Suresh, A. Banerjee, P. K. Ganguly, S. Tata Steel R&D Jamshedpur 831001 Jharkhand India IIT Dept Chem Engn Kharagpur W Bengal India

The main objective of the optimal reagent addition was to maximize the quantity of product with minimal quantity of feed. In the present study, the optimal addition of reagents during the chemical leaching of coal was computed. Chemical leaching of coal was carried out using aqueous solution of caustic to dissolve and remove the mineral matter. Simulation studies were carried out using the optimal reagent addition for chemical leaching of coal in batch reactors. This was experimentally validated, using the bench-scale reactor setup with hierarchical optimization architecture. Chemical leaching experiments were conducted using West Bokaro coal. Samples collected at various time intervals during the experiment were analyzed. Variations in silica (SiO2) and alumina (Al2O3) concentrations, which were main constituents present in coal ash, were evaluated with respect to time for different concentrations of caustic. The simulation studies for optimal addition were carried out at 6, 8 and 10 intervals. An objective function, required for maximum ash removal, was solved, using sequential quadratic programming (SQP) algorithm to find out the optimum sequence for reagent dosing. An improvement of about 1% (wt) ash reduction on an average was observed with implementation of optimal reagent addition.

关键词： coal optimization leaching mineral processing sequential quadratic programming

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An Optimization Applied to Design of SC Biquad-Based Circuits

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RECENT ADVANCES IN ELECTRICAL & ELECTRONIC ENGINEERING 2014年第1期7卷 47-56页

作者： Ngai, Cheong Macau Polytech Inst Rua Gonzaga Gomes Macau Peoples R China

This paper presents a novel optimization technique for the design of multi-stage switched capacitor (SC) biquad-based circuits, using multi-objective constraint programming. Optimization methods, namely single objective and multi-objective in the design areas of SC circuits that are adopted in optimal capacitance assignment are briefly introduced. A sample design (4th order SC biquad-based circuit) with multiple objectives is given for demonstrating the efficiency of the proposed optimization method, which can meet multiple targets (for example, more than two optimal goals- gain of op-amp and size of total capacitance area), showing 6% reduction of total capacitance area, while maintaining the same frequency responses. Also, this paper demonstrates an overview of optimization techniques for the design of different SC biquad-based circuits, using constraint programming. In particular, the progresses achieved on adopting optimization approaches in Operational Amplifiers (OA) are briefly reviewed and then compared.

关键词： Constraint programming capacitance assignment multi-objective optimization sequential quadratic programming SC biquad-based circuits

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An SR1/BFGS SQP algorithm for nonconvex nonlinear programs with block-diagonal Hessian matrix

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MATHEMATICAL programming COMPUTATION 2016年第4期8卷 435-459页

作者： Janka, Dennis Kirches, Christian Sager, Sebastian Wachter, Andreas Heidelberg Univ Interdisciplinary Ctr Sci Comp IWR Neuenheimer Feld 368 D-69120 Heidelberg Germany Otto von Guericke Univ Inst Math Optimizat D-39106 Magdeburg Germany Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

We present a quasi-Newton sequential quadratic programming (SQP) algorithm for nonlinear programs in which the Hessian of the Lagrangian function is block-diagonal. Problems with this characteristic frequently arise in the context of optimal control;for example, when a direct multiple shooting parametrization is used. In this article, we describe an implementation of a filter line-search SQP method that computes search directions using an active-set quadratic programming (QP) solver. To take advantage of the block-diagonal structure of the Hessian matrix, each block is approximated separately by quasi-Newton updates. For nonconvex instances, that arise, for example, in optimum experimental design control problems, these blocks are often found to be indefinite. In that case, the block-BFGS quasi-Newton update can lead to poor convergence. The novel aspect in this work is the use of SR1 updates in place of BFGS approximations whenever possible. The resulting indefinite QPs necessitate an inertia control mechanism within the sparse Schur-complement factorization that is carried out by the active-set QP solver. This permits an adaptive selection of the Hessian approximation that guarantees sufficient progress towards a stationary point of the problem. Numerical results demonstrate that the proposed approach reduces the number of SQP iterations and CPU time required for the solution of a set of optimal control problems.

关键词： Quasi-Newton sequential quadratic programming Direct methods for optimal control Optimum experimental design

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Refined ensemble-based waterflooding optimization subject to field-wide constraints

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COMPUTATIONAL GEOSCIENCES 2020年第2期24卷 871-887页

作者： Tueros, Juan Alberto Rojas Horowitz, Bernardo Willmersdorf, Ramiro Brito de Oliveira, Diego Felipe Barbosa Univ Fed Pernambuco Dept Civil Engn Recife PE Brazil PETROBRAS Petr Brasileiro SA Rio De Janeiro RJ Brazil

In this work, we present a modification (refinement) of the ensemble-based method for constrained waterflooding optimization. The problem of determining life-cycle rate controls for both producer and injector wells that maximize the net present value, NPV, subject to well and field-wide capacity constraints is formulated and solved using sequential quadratic programming, SQP. The required gradient is approximately computed by an ensemble-based method. Field NPV is decomposed as the sum of the NPVs of each well. Sensitivity matrix of well NPVs with respect to controls of all wells is obtained from ensemble-based covariance matrices of controls and of well NPVs to controls. For efficiency reasons, ensemble size should be kept small which results in sampling errors. The approximate gradient is the sum of the columns of the refined sensitivity matrix. Using small-sized ensembles introduces spurious correlations that degrade gradient quality. Novel nondistance-based localization technique is employed to mitigate the deleterious effects of spurious correlations to refine the sensitivity of NPV of production wells with respect to injector controls. The localization technique is based on the connectivity of each injector/producer pair using a producer-based capacitance resistance model (CRMP). Competitiveness coefficients are developed to refine sensitivity of NPV of production wells with respect to producer controls, obtained using an interference test. A new procedure is proposed for consideration of maximum water-cut limit resulting in producer shut-in during the optimization process. Smoothing techniques are also introduced to avoid excessive abrupt jumps in well controls and to improve the overall optimization efficiency. Procedures and refinements are applied to a realistic reservoir taken from the literature, TNO Brugge Field, to demonstrate the resulting level of objective function improvement and variability reduction of the obtained solutions. NPV solution statist

关键词： Large-scale algorithm Ensemble-based method Waterflooding optimization sequential quadratic programming Refined sensitivity matrix Constrained optimization

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Design of Spline-Evolutionary Computing Paradigm for Nonlinear Thin Film Flow Model

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2021年第9期46卷 9279-9299页

作者： Rizwan, Aamir Ahmad, Iftikhar Raja, Muhammad Asif Zahoor Shoaib, Muhammad Univ Gujrat Dept Math Gujrat Pakistan Natl Yunlin Univ Sci & Technol Future Technol Res Ctr 123 Univ RdSect 3 Touliu 64002 Yunlin Taiwan COMSATS Univ Islamabad Dept Elect & Comp Engn Attock Campus Attock 43600 Pakistan COMSATS Univ Islamabad Dept Math Attock Campus Attock 43600 Pakistan

A novel design of stochastic numerical computing method is introduced for computational fluid dynamics problem governed with nonlinear thin film flow (TFF) system by exploiting the competency of polynomial splines for discretization and optimization with evolutionary computing aided with brilliance of local search. The TFF model of second grade fluid is represented with nonlinear second-order differential system. The aim of the present work is to exploit the cubic spline approach (CSA) to transform the differential equations for TFF model into an equivalent set of nonlinear equations. The approximation in mean squared error sense is introduced for the formulation of cost function for solving the nonlinear system of equations representing TFF model. The optimization of the decision variables of the cost function is carried out with global search efficacy of evolution by genetic algorithms (GAs) integrated with sequential quadratic programming (SQP) for speedy adjustments. The designed spline-evolutionary computing paradigm, CSA-GA-SQP, is evaluated for different scenarios of TFF model by variation of second grade and magnetic parameters, as well as variation in the length of splines. Results endorsed the worth of CSA-GA-SQP solver as an efficient alternative, reliable, stable, and accurate framework for the variants of nonlinear TFF systems on the basis of multiple autonomous executions. The design computing spline paradigm CSA-GA-SQP is a promising alternative numerical solver to be implemented for the solution of stiff nonlinear systems representing the complex scenarios of computational fluid dynamics problems.

关键词： Nonlinear thin film flow Evolutionary cubic spline Genetic algorithms sequential quadratic programming Polynomial splines

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A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization

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MATHEMATICAL programming COMPUTATION 2012年第4期4卷 383-412页

作者： Exler, Oliver Lehmann, Thomas Schittkowski, Klaus Univ Bayreuth Dept Comp Sci D-95440 Bayreuth Germany Konrad Zuse Zentrum ZIB D-14195 Berlin Germany

We present numerical results of a comparative study of codes for nonlinear and nonconvex mixed-integer optimization. The underlying algorithms are based on sequential quadratic programming (SQP) with stabilization by trust-regions, linear outer approximations, and branch-and-bound techniques. The mixed-integer quadratic programming subproblems are solved by a branch-and-cut algorithm. Second order information is updated by a quasi-Newton update formula (BFGS) applied to the Lagrange function for continuous, but also for integer variables. We do not require that the model functions can be evaluated at fractional values of the integer variables. Thus, partial derivatives with respect to integer variables are replaced by descent directions obtained from function values at neighboring grid points, and the number of simulations or function evaluations, respectively, is our main performance criterion to measure the efficiency of a code. Numerical results are presented for a set of 100 academic mixed-integer test problems. Since not all of our test examples are convex, we reach the best-known solutions in about 90 % of the test runs, but at least feasible solutions in the other cases. The average number of function evaluations of the new mixed-integer SQP code is between 240 and 500 including those needed for one-or two-sided approximations of partial derivatives or descent directions, respectively. In addition, we present numerical results for a set of 55 test problems with some practical background in petroleum engineering.

关键词： MINLP Mixed-integer nonlinear programming SQP sequential quadratic programming Trust region method Linear outer approximation MIQP Mixed-integer quadratic programming Numerical algorithms Performance evaluation Mixed-integer test problems Engineering optimization

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Smooth SQP methods for mathematical programs with nonlinear complementarity constraints

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SIAM JOURNAL ON OPTIMIZATION 2000年第3期10卷 779-808页

作者： Jiang, HY Ralph, D Univ Melbourne Dept Math & Stat Parkville Vic 3052 Australia

Mathematical programs with nonlinear complementarity constraints are reformulated using better posed but nonsmooth constraints. We introduce a class of functions, parameterized by a real scalar, to approximate these nonsmooth problems by smooth nonlinear programs. This smoothing procedure has the extra benefits that it often improves the prospect of feasibility and stability of the constraints of the associated nonlinear programs and their quadratic approximations. We present two globally convergent algorithms based on sequential quadratic programming (SQP) as applied in exact penalty methods for nonlinear programs. Global convergence of the implicit smooth SQP method depends on existence of a lower-level nondegenerate (strictly complementary) limit point of the iteration sequence. Global convergence of the explicit smooth SQP method depends on a weaker property, i.e., existence of a limit point at which a generalized constraint qualification holds. We also discuss some practical matters relating to computer implementations.

关键词： mathematical programs with equilibrium constraints bilevel optimization complementarity problems sequential quadratic programming exact penalty generalized constraint qualification global convergence smoothing method

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Semismooth SQP method for equality-constrained optimization problems with an application to the lifted reformulation of mathematical programs with complementarity constraints

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OPTIMIZATION METHODS & SOFTWARE 2011年第4-5期26卷 847-872页

作者： Izmailov, A. F. Pogosyan, A. L. Solodov, M. V. IMPA Inst Matemat Pura Aplicada BR-22460320 Rio De Janeiro RJ Brazil Moscow MV Lomonosov State Univ MSU OR Dept VMK Fac Moscow 119991 Russia

We consider the sequential quadratic programming (SQP) algorithm applied to equality-constrained optimization problems, where the problem data is differentiable with Lipschitz-continuous first derivatives. For this setting, Dennis-More-type analysis of primal superlinear convergence is presented. Our main motivation is a special modification of SQP tailored to the structure of the lifted reformulation of mathematical programs with complementarity constraints (MPCC). For this problem, we propose a special positive definite modification of the matrices in the generalized Hessian, which is suitable for globalization of SQP based on the penalty function, and at the same time can be expected to satisfy our general Dennis-More-type conditions, thus preserving local superlinear convergence. (Standard quasi-Newton updates in the SQP framework require twice differentiability of the problem data at the solution for superlinear convergence.) Preliminary numerical results comparing a number of quasi-Newton versions of semismooth SQP applied to MPCC are also reported.

关键词： sequential quadratic programming semismoothness B-differential BD-regularity semismooth Newton method second-order sufficiency mathematical programs with complementarity constraints

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Optimal signal sets for non-Gaussian detectors

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SIAM JOURNAL ON OPTIMIZATION 1999年第2期9卷 316-326页

作者： Gockenbach, MS Kearsley, AJ Univ Michigan Dept Math Ann Arbor MI 48109 USA Carnegie Mellon Univ Dept Math Sci Pittsburgh PA 15213 USA

Identifying a maximally separated set of signals is important in the design of modems. The notion of optimality is dependent on the model chosen to describe noise in the measurements;while some analytic results can be derived under the assumption of Gaussian noise, no such techniques are known for choosing signal sets in the non-Gaussian case. To obtain numerical solutions for non-Gaussian detectors, minimax problems are transformed into nonlinear programs, resulting in a novel formulation yielding problems with relatively few variables and many inequality constraints. Using sequential quadratic programming, optimal signal sets are obtained for a variety of noise distributions.

关键词： optimal design inequality constraints sequential quadratic programming

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