Nonmonotone bundle-type scheme for convex nonsmooth minimization

In this paper, we present a general scheme for bundle-type algorithms which includes a nonmonotone line search procedure and for which global convergence can be proved. Some numerical examples are reported, showing that the nonmonotonicity can be beneficial from a computational point of view.This work was partially supported by the National Research Program on Metodi di ottimizzazione per le decisioni, Ministero dell' Universitá e della Ricerca Scientifica e Tecnologica and by ASI: Agenzia Spaziale Italiana.     

Quantitative stability of variational systems: III.ε-approximate solutions

We prove that the-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that the-subgradient mapping is Lipschitz continuous.Research supported in part by the National Science Foundation and the Air Force Office of Scientific Research.     

A generalized Dantzig—Wolfe decomposition principle for a class of nonconvex programming problems

Since Dantzig—Wolfe's pioneering contribution, the decomposition approach using a pricing mechanism has been developed for a wide class of mathematical programs. For convex programs a linear space of Lagrangean multipliers is enough to define price functions. For general mathematical programs the price functions could be defined by using a subclass of nondecreasing functions. However the space of nondecreasing functions is no longer finite dimensional. In this paper we consider a specific nonconvex optimization problem min {f(x):h _j (x)g(x),j=1, ,m, xX}, wheref(·),h _j (·) andg(·) are finite convex functions andX is a closed convex set. We generalize optimal price functions for this problem in such a way that the parameters of generalized price functions are defined in a finite dimensional space. Combining convex duality and a nonconvex duality we can develop a decomposition method to find a globally optimal solution.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.     

A smooth method for the finite minimax problem

We consider unconstrained minimax problems where the objective function is the maximum of a finite number of smooth functions. We prove that, under usual assumptions, it is possible to construct a continuously differentiable function, whose minimizers yield the minimizers of the max function and the corresponding minimum values. On this basis, we can define implementable algorithms for the solution of the minimax problem, which are globally convergent at a superlinear convergence rate. Preliminary numerical results are reported.This research was partially supported by the National Research Program on Metodi di ottimizzazione per le decisioni, Ministero dell'Università e della Ricerca Scientifica e Tecnologica, Italy.     

On the global optimization properties of finite-difference local descent algorithms

The paper is devoted to the convergence properties of finite-difference local descent algorithms in global optimization problems with a special -convex structure. It is assumed that the objective function can be closely approximated by some smooth convex function. Stability properties of the perturbed gradient descent and coordinate descent methods are investigated. Basing on this results some global optimization properties of finite-difference local descent algorithms, in particular, coordinate descent method, are discovered. These properties are not inherent in methods using exact gradients.The paper was presented at the II. IIASA-Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Optimization of Glycosylation Reactions in a Microreactor

Glycosylations are notoriously difficult reactions that require extensive optimization regarding the type of anomeric leaving group, solvent, reaction temperature, and reaction time. Described is the use of a silicon‐based microreactor to screen reaction conditions and to scale‐up synthetic procedures. For the first time, glycosyl phosphates were employed in a microreactor. The optimized reaction conditions were successfully transferred to a batch process.     

Exact rotamer optimization for protein design

Computational methods play a central role in the rational design of novel proteins. The present work describes a new hybrid exact rotamer optimization (HERO) method that builds on previous dead-end elimination algorithms to yield dramatic performance enhancements. Measured on experimentally validated physical models, these improvements make it possible to perform previously intractable designs of entire protein core, surface, or boundary regions. Computational demonstrations include a full core design of the variable domains of the light and heavy chains of catalytic antibody 48G7 FAB with 74 residues and 10(128) conformations, a full core/boundary design of the beta1 domain of protein G with 25 residues and 10(53) conformations, and a full surface design of the beta1 domain of protein G with 27 residues and 10(60) conformations. In addition, a full sequence design of the beta1 domain of protein G is used to demonstrate the strong dependence of algorithm performance on the exact form of the potential function and the fidelity of the rotamer library. These results emphasize that search algorithm performance for protein design can only be meaningfully evaluated on physical models that have been subjected to experimental scrutiny. The new algorithm greatly facilitates ongoing efforts to engineer increasingly complex protein features.     

Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm

We present a Monte Carlo algorithm to find approximate solutions of the traveling salesman problem. The algorithm generates randomly the permutations of the stations of the traveling salesman trip, with probability depending on the length of the corresponding route. Reasoning by analogy with statistical thermodynamics, we use the probability given by the Boltzmann-Gibbs distribution. Surprisingly enough, using this simple algorithm, one can get very close to the optimal solution of the problem or even find the true optimum. We demonstrate this on several examples.We conjecture that the analogy with thermodynamics can offer a new insight into optimization problems and can suggest efficient algorithms for solving them.The author acknowledges stimulating discussions with J. Piút concerning the main ideas of the present paper. The author is also indebted to P. Brunovský, J. erný, M. Hamala, . Peko, . Znám, and R. Zajac for useful comments.     

Global optimization and stochastic differential equations

Let ⁿ be then-dimensional real Euclidean space,x=(x ₁,x ₂, ...,x _n)^{T n} , and letf: ⁿ R be a real-valued function. We consider the problem of finding the global minimizers off. A new method to compute numerically the global minimizers by following the paths of a system of stochastic differential equations is proposed. This method is motivated by quantum mechanics. Some numerical experience on a set of test problems is presented. The method compares favorably with other existing methods for global optimization.This research has been supported by the European Research Office of the US Army under Contract No. DAJA-37-81-C-0740.The third author gratefully acknowledges Prof. A. Rinnooy Kan for bringing to his attention Ref. 4.     

Optimization and validation of an enzyme immunoassay for the insect growth regulator fenoxycarb

A competitive enzyme-linked immunosorbent assay (ELISA) was developed for the quantitative detection of the insect growth regulator fenoxycarb. Polyclonal rabbit antisera, raised against protein conjugates of four haptenic derivatives of fenoxycarb, were utilized in immobilized antigen-based, competitive immunoassays. With ELISA systems that were both hapten- and carrier-heterologous, most antiserum titers fell in the range of 1:1000-1:30,000. Assay conditions, including concentrations of antisera and coating antigens, were optimized. The effect of pH, organic solvents, and various blocking agents was also investigated. A hapten-homologous and two hapten-heterologous indirect ELISAs allowed fenoxycarb determination in the range of 0.1-85 ng ml⁻¹ with apparent IC₅₀ values of 1.2-2.8 ng ml⁻¹. Cross-reactivities with a number of compounds (e.g. pesticides of related structure, hapten synthesis intermediates, fenoxycarb metabolite, photodegradation products) were determined, and the assay proved highly selective for fenoxycarb. In particular, no significant interference was found with selected pyrethroid and juvenile hormone analog insecticides, phenoxyacetic acid herbicides, and photodegradation products of fenoxycarb. Using spiked water samples, assay performance was validated by SPME/GC-MS.