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CONOPT—A Large-Scale GRG Code
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1994
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Mathematical ProgrammingLarge-scale Global OptimizationComputational ScienceEngineeringContinuous OptimizationApproximation TheoryCode GenerationNonlinear ProgrammingGrg CodeGrg AlgorithmGeneralized Reduced-gradientComputer EngineeringComputer ScienceNonlinear OptimizationParallel ComputingCombinatorial OptimizationUnconstrained OptimizationSoftware Analysis
CONOPT is a generalized reduced‑gradient algorithm designed to solve large‑scale nonlinear programs with sparse nonlinear constraints. The paper examines strategic and tactical decisions made during the development, upgrade, and maintenance of CONOPT over the past eight years. The authors compare GRG to sequential linearized subproblem methods and discuss key implementation components such as basis factorizations, search directions, line‑searches, and Newton iterations. Performance statistics for up to 4000‑equation models from engineering and economics show that GRG codes are competitive with other solvers in efficiency and reliability, especially for highly nonlinear constraints where feasibility is hard to achieve. Published in the INFORMS Journal on Computing (ISSN 1091‑9856), formerly the ORSA Journal on Computing (ISSN 0899‑1499).
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.