Strongly polynomial-time approximation for a class of bicriteria problems

Consider the following problem: given a ground set and two minimization objectives of the same type find a subset from a given subset-class that minimizes the first objective subject to a budget constraint on the second objective. Using Megiddo's parametric method we improve an earlier weakly polynomial time algorithm.     

A closed-form representation of mixed-integer program value functions

We identify a class of formulas computable in polynomial time such that the functions defined by these formulas are precisely the value functions of mixed-integer programs with rational constraint coefficients.     

Noncollinear optical parametric amplification in lithium triborate seeded by a cw Ti:sapphire laser

Experimental investigations of a type-I noncollinear phase-matched optical parametric amplification based on lithium triborate, which was pumped by a 5-ns second-harmonic pulses from a Q-switched Nd:YAG, seeded by a cw Ti:sapphire laser at 800 nm, was presented. The experiments generated 2-ns signal output pulses at 800 nm, the maximum signal output pulse energy reached 19 μJ, the corresponding parametric gain was 44 dB. Furthermore, the experiments demonstrate that the 65 nm-FWHM parametric fluorescence gain spectrum could also be observed. A quantitative account of the ultrabroadband parametric fluorescence gain spectrum was given with our theory. The experimental measurements are in agreement with theoretical calculations.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

Algorithms for flows with parametric capacities

We consider the problem of finding maximal flows with respect to capacities which are linear functions of a parametert [0,T]. Since this problem is a special case of a parametric linear program the classichorizontal approach can be applied in which optimal solutions are computed for successive subintervals of [0,T]. We discuss an alternative algorithm which approximates in each iteration the optimal solution for allt [0,T]. Thisvertical algorithm is a labeling type algorithm where the flow variables are piecewise linear functions. Flow augmentations are done alongconditional flow augmenting paths which can be found by modified path algorithms. The vertical algorithm can be used to solve the parametric flow problem optimally as well as to compute a good approximation for allt if the computation of the optimal solution turns out to be too time consuming.Partially supported by NSF Grants ECS-8412926 and INT-8521433, and NATO Grant RG 85/0240.     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

Dynamical instability of laminated plates with external cutout

A method to study dynamical instability and non-linear parametric vibrations of symmetrically laminated plates of complex shapes and having different cutouts is proposed. The first-order shear deformation theory (FSDT) and the classical plate theory (CPT) are used to formulate a mathematical statement of the given problem. The presence of cutouts essentially complicates the solution of buckling problem, since the stress field is non-uniform. At first, a plane stress analysis is carried out using the variational Ritz method and the R-functions theory. The obtained results are applied to investigate buckling and parametric vibrations of laminated plates. The developed method uses the R-functions theory, and it may be directly employed to study laminated plates of arbitrary forms and different boundary conditions. Besides, the proposed method is numerical-analytical, what greatly facilitates a solution of similar-like non-linear problems. In order to show the advantage of the developed approach, instability zones and response curves for the layered cross- and angle-ply plates with external cutouts are constructed and discussed.     

How gamma radiation processing systems are benefiting from the latest advances in information technology

This paper discusses how gamma irradiation plants are putting the latest advances in computer and information technology to use for better process control, cost savings, and strategic advantages.

Some irradiator operations are gaining significant benefits by integrating computer technology and robotics with real-time information processing, multi-user databases, and communication networks. The paper reports on several irradiation facilities that are making good use of client/server LANs, user-friendly graphics interfaces, supervisory control and data acquisition (SCADA) systems, distributed I/O with real-time sensor devices, trending analysis, real-time product tracking, dynamic product scheduling, and automated dosimetry reading. These plants are lowering costs by fast and reliable reconciliation of dosimetry data, easier validation to GMP requirements, optimizing production flow, and faster release of sterilized products to market.

There is a trend in the manufacturing sector towards total automation using “predictive process control”. Real-time verification of process parameters “on-the-run” allows control parameters to be adjusted appropriately, before the process strays out of limits. Applying this technology to the gamma radiation process, control will be based on monitoring the key parameters such as time, and making adjustments during the process to optimize quality and throughput. Dosimetry results will be used as a quality control measurement rather than as a final monitor for the release of the product. Results are correlated with the irradiation process data to quickly and confidently reconcile variations. Ultimately, a parametric process control system utilizing responsive control, feedback and verification will not only increase productivity and process efficiency, but can also result in operating within tighter dose control set points.     

Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically non-convex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q. In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the ${?}_1$-norm of q.