CONOPT is a generalized reduced-gradient (GRG) algorithm for solving large-scale nonlinear programs involving sparse nonlinear constraints. The paper will discuss strategic and tactical decisions in the development, upgrade, and maintenance of CONOPT over the last 8 years. A verbal and intuitive comparison of the GRG algorithm with the popular methods based on sequential linearized subproblems forms the basis for discussions of the implementation of critical components in a GRG code: basis factorizations, search directions, line-searches, and Newton iterations. The paper contains performance statistics for a range of models from different branches of engineering and economics of up to 4000 equations with comparative figures for MINOS version 5.3. Based on these statistics the paper concludes that GRG codes can be very competitive with other codes for large-scale nonlinear programming from both an efficiency and a reliability point of view. This is especially true for models with fairly nonlinear constraints, particularly when it is difficult to attain feasibility. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

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The paper describes a new computerized collection of test models for mixed-integer nonlinear programming. Because there is no standard format for nonlinear models, the model collection is augmented with a translation server that can transform the models from their basic GAMS format into other formats, including AMPL, BARON, LGO, LINGO, and MINOPT. The translation server can also be used to transform industrial models that contain confidential information. Such transformations allow many of these models to be distributed to the research community as highly relevant algorithmic test models.

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We formulate the problem of optimally adjusting the components of a large matrix to satisfy consistency requirements as a nonlinear network optimization model. An efficient network optimization algorithm-GEiNOSis incorporated in a user friendly modeling system-GAMS. The resulting software is used for balancing large Social Accounting Matrices (SAM). We assemble a library of SAM models from developing countries and report computational results.