CONOPT—A Large-Scale GRG Code

Abstract

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.

Convexity and Solutions of Stochastic Multidimensional 0-1 Knapsack Problems with Probabilistic Constraints

“…Since lim x→−∞ f (x) = 0 and f (x 1 ) < 0, there exists x 2 ∈ (−∞, x 1 ) such that f (x 1 ) < f (x 2 ) < 0 and f (x 2 ) < 0, which contradicts (3.14). 4 The positivity and the decreasing property follows directly from 2. To prove the strict convexity we show the following inequality:…”

“…We used GAMS [11] as a modeling system with DICOPT [16] as a MINLP solver. We selected CPLEX [18] as a mixed-integer linear programming (MILP) solver and CONOPT [4,5] as a nonlinear programming (NLP) solver both called internally from DICOPT in solving subproblems. GAMS has built-in support for various special math functions including the regularized gamma function, the regularized beta function, and the standard normal c.d.f., which cover all of our cases.…”

Identification of optimal measurement sets for complete flux elucidation in metabolic flux analysis experiments

“…The program was run on a Linux cluster box of four 2.6 GHz Pentium 4 processors with 8 GB memory. TestUniq and TestOpt were solved using GAMS/CONOPT 3 (Drud, 1994). GAMS/BARON 7.5 (Tawarmalani and Sahinidis, 2004) and the EMU representation were also used whenever possible to ensure global optimality during the verification process.…”

A polynomial optimization approach to constant rebalanced portfolio selection

“…The results of computational experiments are given in Sect. 4. Concluding remarks are given in Sect.…”

“…We conduct computational experiments, and assess the benefit of our cutting plane approach in comparison with the global optimization solver over polynomials GloptiPoly [7], the global optimization solver BARON [24], and the nonlinear programming (NLP) solver CONOPT [4]. GloptiPoly, which builds up a hierarchy of SDP relaxations (see [15]), successfully provides a globally optimal solution of small-size problems.…”