1,721,075 research outputs found
A parameter-free unconstrained reformulation for nonsmooth problems with convex constraints
Full text linkIn the present paper we propose to rewrite a nonsmooth problem subjected to convex constraints as an unconstrained problem. We show that this novel formulation shares the same global and local minima with the original constrained problem. Moreover, the reformulation can be solved with standard nonsmooth optimization methods if we are able to make projections onto the feasible sets. Numerical evidence shows that the proposed formulation compares favorably against state-of-art approaches. Code can be found at https://github.com/jth3galv/dfppm
An algorithmic framework based on primitive directions and nonmonotone line searches for black-box optimization problems with integer variables
Full text linkIn this paper, we develop a new algorithmic framework to solve black-box problems with integer variables. The strategy included in the framework makes use of specific search directions (so called primitive directions) and a suitably developed nonmonotone line search, thus guaranteeing a high level of freedom when exploring the integer lattice. First, we describe and analyze a version of the algorithm that tackles problems with only bound constraints on the variables. Then, we combine it with a penalty approach in order to solve problems with simulation constraints. In both cases we prove finite convergence to a suitably defined local minimum of the problem. We report extensive numerical experiments based on a test bed of both bound-constrained and generally-constrained problems. We show the effectiveness of the method when compared to other state-of-the-art solvers for black-box integer optimization
Solving non-monotone equilibrium problems via a DIRECT-type approach
Full text linkA global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of the DIRECT algorithm, which exploits local bounds of the Lipschitz constant of the objective function, with local minimizations. Unlike most existing solution methods for EPs, no monotonicity-type condition is assumed in this paper. Preliminary numerical results on several classes of EPs show the effectiveness of the approach
A DIRECT-based approach exploiting local minimizations for the solution of large-scale global optimization problems
No full textIn this paper we propose a new algorithm for solving difficult large-scale global optimization problems. We draw our inspiration from the well-known DIRECT algorithm which, by exploiting the objective function behavior, produces a set of points that tries to cover the most interesting regions of the feasible set. Unfortunately, it is well-known that this strategy suffers when the dimension of the problem increases. As a first step we define a multi-start algorithm using DIRECT as a deterministic generator of starting points. Then, the new algorithm consists in repeatedly applying the previous multi-start algorithm on suitable modifications of the variable space that exploit the information gained during the optimization process. The efficiency of the new algorithm is pointed out by a consistent numerical experimentation involving both standard test problems and the optimization of Morse potential of molecular clusters. © 2008 Springer Science+Business Media, LLC
An Augmented Lagrangian Method Exploiting an Active-Set Strategy and Second-Order Information
Full text linkIn this paper, we consider nonlinear optimization problems with nonlinear equality constraints and bound constraints on the variables. For the solution of such problems, many augmented Lagrangian methods have been defined in the literature. Here, we propose to modify one of these algorithms, namely ALGENCAN by Andreani et al., in such a way to incorporate second-order information into the augmented Lagrangian framework, using an active-set strategy. We show that the overall algorithm has the same convergence properties as ALGENCAN and an asymptotic quadratic convergence rate under suitable assumptions. The numerical results confirm that the proposed algorithm is a viable alternative to ALGENCAN with greater robustness
A nonmonotone truncated Newton-Krylov method exploiting negative curvature directions, for large scale unconstrained optimization
No full textWe propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of
search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative curvature direction. A test based on the quadratic model of the objective function is used to select the most promising between
the two search directions. Both the latter selection rule and the CG stopping criterion for approximately solving Newton’s equation, strongly rely on conjugacy conditions.
An appropriate linesearch technique is adopted for each search direction: a nonmonotone stabilization is used with the approximate Newton step, while an Armijo type
linesearch is used for the negative curvature direction. The proposed algorithm is both globally and superlinearly convergent to stationary points satisfying second order necessary
conditions. We carry out a significant numerical experience in order to test our proposal
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
On necessary optimality conditions for sets of points in multiobjective optimization
Full text linkTaking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been devised, following the real nature of multiobjective optimization, where the aim is that of approximating the efficient set. This calls for a new analysis of the necessary optimality conditions for multiobjective optimization. We explore conditions for sets of points that share the same features of the necessary optimality conditions for single-objective optimization. On the one hand, from a theoretical point of view, these conditions define properties that are necessarily satisfied by the (weakly) efficient set. On the other hand, from an algorithmic point of view, any set that does not satisfy the proposed conditions can be easily improved by using first-order information on some objective functions. We analyse both the unconstrained and the constrained case, giving some examples
Data and performance of an active-set truncated Newton method with non-monotone line search for bound-constrained optimization
Full text linkIn this data article, we report data and experiments related to the research article entitled “A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization”, by Cristofari et al. (2017). The method proposed in Cristofari et al. (2017), tackles optimization problems with bound constraints by properly combining an active-set estimate with a truncated Newton strategy. Here, we report the detailed numerical experience performed over a commonly used test set, namely CUTEst (Gould et al., 2015). First, the algorithm ASA-BCP proposed in Cristofari et al. (2017) is compared with the related method NMBC (De Santis et al., 2012). Then, a comparison with the renowned methods ALGENCAN (Birgin and Martínez et al., 2002) and LANCELOT B (Gould et al., 2003) is reported
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