A Trust Region Strategy for Equality Constrained Optimization

Celis, Maria Rosa; Dennis, J. E.; Tapia, J E

doi:10.21236/ada454933

Cited by 127 publications

(162 citation statements)

References 4 publications

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“…This has the flavor of condition (5.13). Celis, Dennis and Tapia [9] also impose a constraint of the form (6.21), but define ζ as the value h(x) + ∇h(x) T d C 2 , where d C is a Cauchy step for problem (6.20). In this respect it is different from the approaches considered earlier in the paper which aim for at least a fraction of the optimal linear decrease, whereas Celis, Dennis and Tapia are satisfied with a more modest decrease.…”

Section: Balancing Feasibility and Optimality In Othermentioning

confidence: 99%

Steering exact penalty methods for nonlinear programming

Byrd

Nocedal

Waltz

2008

Optimization Methods and Software

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This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be a heuristic and is determined, instead, by a subproblem with clearly defined objectives. The new penalty update strategy is presented in the context of sequential quadratic programming (SQP) and sequential linear-quadratic programming (SLQP) methods that use trust regions to promote convergence. The paper concludes with a discussion of penalty parameters for merit functions used in line search methods.

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Section: Balancing Feasibility and Optimality In Othermentioning

confidence: 99%

Steering exact penalty methods for nonlinear programming

Byrd

Nocedal

Waltz

2008

Optimization Methods and Software

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“…As an illustration/application, one may mention the Celis-Dennis-Tapia (CDT) problem [9], to minimize a non-convex quadratic function over the intersection of two ellipsoids, which can be turned into an instance of the problem above by introducing a new dummy variable. Such problems arise naturally in iterative non-linear optimization procedures where in one iteration step, the objective function and the constraints are approximated by quadratic models.…”

Section: Minimization Problemsmentioning

confidence: 99%

Bit complexity for multi-homogeneous polynomial system solving—Application to polynomial minimization

Din

Schost

2018

Journal of Symbolic Computation

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Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input system, under some genericity assumptions. The assumptions essentially imply that the Jacobian matrix of the system under study has maximal rank at the solution set and that this solution set is finite. The algorithm is probabilistic and a probability analysis is provided.Next, we apply these results to the problem of optimizing a linear map on the real trace of an algebraic set. Under some genericity assumptions, we provide bit complexity estimates for solving this polynomial minimization problem.

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“…Third, the domain of permissible solutions is not limited to variables satisfying some equality or inequality constraints, therefore it is an unconstrained problem. In the literature, there are many methods and algorithms developed to solve the multidimensional unconstrained non-linear problem, such as Newton's method, Broyden's method (Broyden 1965), line-search methods, trust-region methods (Celis, Dennis, and Tapia 1985), the Nelder-Mead simplex method (Nelder and Mead 1965), the conjugate-gradient method (Hestenes and Stiefel 1952) and their variants (Fan and Zahara 2007;Birgin and Martinez 2001). Most of these algorithms involve an iterative process that converges on a sufficiently accurate solution.…”

Section: Multidimensional Unconstrained Non-linear Minimizationmentioning

confidence: 99%

An optimization technique for addressing DEM misregistration in hilly terrain

Goodchild

2015

Annals of GIS

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Digital elevation models (DEMs) represent the Earth's topography and support a variety of applications, ranging from extracting watershed drainage structure to measuring glacier volume. Applications that require conflation of multiple DEMs are problematic, however, because of misregistration. We explore a spatial optimization technique to quantify the misregistration on the pixel level between NASA's Shuttle Radar Topography Mission (SRTM) elevation data set and the USGS's National Elevation Dataset (NED). The misregistration, estimated within blocks by horizontal offset and direction, is modelled spatially in terms of typical topographical parameters: slope, aspect and elevation. A Nelder-Mead algorithm was implemented to compute the local shift at two study sites in the San Gabriel Mountains (SGM) and Santa Monica Mountains (SMM) in Los Angeles County, California. The magnitude of misregistration is generally less than the distance between DEM postings, and varies by terrain type, being larger in steeper terrains; nevertheless, misregistration is systematic within these continuous terrains that have similar topographical features. ARTICLE HISTORY

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A Trust Region Strategy for Equality Constrained Optimization

Cited by 127 publications

References 4 publications

Steering exact penalty methods for nonlinear programming

Steering exact penalty methods for nonlinear programming

Bit complexity for multi-homogeneous polynomial system solving—Application to polynomial minimization

An optimization technique for addressing DEM misregistration in hilly terrain

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