Showing papers in "Optimization Methods & Software in 1996"
TL;DR: In this article, a simple scheme is proposed for handling nonlinear equality constraints in the context of a previously introduced sequential quadratic programming (SQP) algorithm for inequality constrained problems, generating iterates satisfying the constraints.
Abstract: A simple scheme is proposed for handling nonlinear equality constraints in the context of a previously introduced sequential quadratic programming (SQP) algorithm for inequality constrained problems, generating iterates satisfying the constraints. The key is an idea due to Mayne and Polak (Math. Progr., vol. 11, pp. 67-80, 1976) by which nonlinear equality constraints are treated as “≥”-type constraints to be satisfied by all iterates, thus precluding any positive value, and an exact penalty term is added to the objective function, thus penalizing negative values. Mayne and Polak obtained a suitable value of the penalty parameter by iterative adjustments based on a test involving estimates of the KKT multipliers. We argue that the SQP framework allows for a more effective estimation of these multipliers, and we provide convergence analysis of the resulting algorithm. Numerical results, obtained with the CFSQP code, are reported
88 citations
TL;DR: This work analyzes the trust region approach for conic models and presents necessary and sufficient conditions for the solution of the associated trust region subproblems, and proves that the proposed method has global convergence and Q-superlinear convergence properties.
Abstract: A trust region method for conic models to solve unconstrained optimization problems is proposed. We analyze the trust region approach for conic models and present necessary and sufficient conditions for the solution of the associated trust region subproblems. A corresponding numerical algorithm is developed and has been tested for 19 standard test functions in unconstrained optimization. The numerical results show that this method is superior to some advanced methods in the current software libraries. Finally, we prove that the proposed method has global convergence and Q-superlinear convergence properties
54 citations
TL;DR: In this paper necessary and sufficient conditions for the absence of breakdown are obtained in terms of the underlying Krylov sequences for both the Lanczos version and the Hestenes-Stiefel version of the block CG algorithm.
Abstract: It is well-known that when methods of conjugate gradient type are applied to non-symmetric or indefinite symmetric systems, breakdown can occur due to division by zero even if exact arithmetic is used. In this paper necessary and sufficient conditions for the absence of breakdown are obtained in terms of the underlying Krylov sequences for both the Lanczos version and the Hestenes-Stiefel version of the block CG algorithm. These conditions are then related to the definiteness or otherwise of the fundamental matrices that define the algorithm and the Lanczos versions are shown to be inherently more stable than the Hestenes-Stiefel ones. Finally the robustness of several well-known special cases of the algorithm is assessed in the light of the results obtained previously
11 citations
TL;DR: A detailed description of a path-following Interior point algorithm for constrained convex programs is presented, which employs a truncated logarithmic Barrier function, which is particularly suitable to problems with many nonactive constraints.
Abstract: A detailed description of a path-following Interior point algorithm for constrained convex programs is presented. The algorithm employs a truncated logarithmic Barrier function, which is particularly suitable to problems with many nonactive constraints. A special version of the algorithm is adopted to minmax problems. Extensive testing of the algorithms on large-scale Structural Optimization problems (truss topology design, shape design with optimized material) demonstrate their efficiency
8 citations
TL;DR: The impact and the usefulness of difference convex optimization techniques for the numerical solution of problems arising in nonsmooth and nonconvex computational mechanics are investigated in this paper.
Abstract: The impact and the usefulness of difference convex optimization techniques for the numerical solution of problems arising in nonsmooth and nonconvex computational mechanics are investigated in this paper. Algorithms for the numerical solution of the problem are proposed and studied. The relation to the more general quasi- and co-differentiable optimization techniques is also discussed. The link to classical, smooth and nonsmooth computational mechanics’thms is also presented
7 citations
TL;DR: This paper shows that dynamic exploitation of the sparsity inherent in derivative computation can result in dramatic gains in runtime and memory savings, and reports on the runtime andMemory requirements of computing the gradients with the ADIFOR.
Abstract: Automatic differentiation (AD) is a technique that augments computer codes with statements for the computation of derivatives. The computational workhorse of AD-generated codes for first-order derivatives is the linear combination of vectors. For many large-scale problems, the vectors involved in this operation are inherently sparse. If the underlying function is a partially separable one (e.g., if its Hessian is sparse), many of the intermediate gradient vectors computed by AD will also be sparse, even though the final gradient is likely to be dense. For large Jacobians computations, every intermediate derivative vector is usually at least as sparse as the least sparse row of the final Jacobian. In this paper, we show that dynamic exploitation of the sparsity inherent in derivative computation can result in dramatic gains in runtime and memory savings. For a set of gradient problems exhibiting implicit sparsity, we report on the runtime and memory requirements of computing the gradients with the ADIFOR (...