A new computational method for the functional inequality constrained minimax optimization problem

AbstractIn this paper, we consider a general class of functional inequality constrained minimax optimization problems. This problem is first converted into a semi-infinite programming problem. Then, an auxiliary cost function is constructed based on a positive saturated function. The smallest zero of this auxiliary cost function is equal to the minimal cost of the semi-infinite programming problem. However, this auxiliary cost function is nonsmooth. Thus, a smoothing function is introduced. Then, an efficient computational procedure is developed to estimate the smallest zero of this auxiliary cost function. Furthermore, an error bound is obtained to validate the accuracy of the approximate solution. For illustration, two numerical examples are solved using the proposed approach

Well-posedness of Bimodal State-based Switched Systems

AbstractIn this work, we consider the well-posedness of state-based switched systems in the sense of piecewise classical solutions which commonly arise in the control of hybrid systems. We give some necessary and sufficient conditions for the well-posedness of this class of systems. These results can be used as tools for excluding the bimodal system having a Zeno state

A remark on a standard and linear vector network equilibrium problem with capacity constraints

2007-2008 > Academic research: refereed > Publication in refereed journa

Higher order weak epiderivatives and applications to duality andoptimality conditions

AbstractIn this paper, the notions of higher order weak contingent epiderivative and higher order weak adjacent epiderivative for a set-valued map are defined. By virtue of higher order weak adjacent (contingent) epiderivatives and Henig efficiency, we introduce a higher order Mond–Weir type dual problem and a higher order Wolfe type dual problem for a constrained set-valued optimization problem (SOP) and discuss the corresponding weak duality, strong duality and converse duality properties. We also establish higher order Kuhn–Tucker type necessary and sufficient optimality conditions for (SOP)

Atomic detail visualization of photosynthetic membranes with GPU-accelerated ray tracing

The cellular process responsible for providing energy for most life on Earth, namely, photosynthetic light-harvesting, requires the cooperation of hundreds of proteins across an organelle, involving length and time scales spanning several orders of magnitude over quantum and classical regimes. Simulation and visualization of this fundamental energy conversion process pose many unique methodological and computational challenges. We present, in two accompanying movies, light-harvesting in the photosynthetic apparatus found in purple bacteria, the so-called chromatophore. The movies are the culmination of three decades of modeling efforts, featuring the collaboration of theoretical, experimental, and computational scientists. We describe the techniques that were used to build, simulate, analyze, and visualize the structures shown in the movies, and we highlight cases where scientific needs spurred the development of new parallel algorithms that efficiently harness GPU accelerators and petascale computers

Calculations on the Size Effects of Raman Intensities of Silicon Quantum Dots

Raman intensities of Si quantum dots (QDs) with up to 11,489 atoms (about 7.6 nm in diameter) for different scattering configurations are calculated. First, phonon modes in these QDs, including all vibration frequencies and vibration amplitudes, are calculated directly from the lattice dynamic matrix by using a microscopic valence force field model combined with the group theory. Then the Raman intensities of these quantum dots are calculated by using a bond-polarizability approximation. The size effects of the Raman intensity in these QDs are discussed in detail based on these calculations. The calculations are compared with the available experimental observation. We are expecting that our calculations can further stimulate more experimental measurements.Comment: 21 pages, 7 figure

A sequential quadratic penalty method for nonlinear semidefinite programming

2003-2004 > Academic research: refereed > Publication in refereed journa

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

A switched system is a dynamic system that operates by switching between different subsystems or modes. Such systems exhibit both continuous and discrete characteristics—a dual nature that makes designing effective control policies a challenging task. The purpose of this paper is to review some of the latest computational techniques for generating optimal control laws for switched systems with nonlinear dynamics and continuous inequality constraints. We discuss computational strategiesfor optimizing both the times at which a switched system switches from one mode to another (the so-called switching times) and the sequence in which a switched system operates its various possible modes (the so-called switching sequence). These strategies involve novel combinations of the control parameterization method, the timescaling transformation, and bilevel programming and binary relaxation techniques. We conclude the paper by discussing a number of switched system optimal control models arising in practical applications