Yi Shang. Global Search Methods for Solving Nonlinear Optimization Problems. PhD thesis, University of Illinois at Urbana-Champaign, 1997. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Global Optimization For Constrained Nonlinear Programming - Wang (2001) (5 citations) (Correct)
....1.3. According to strategies utilized to escape from local minima, global search approaches can be either deterministic or stochastic. Deterministic global search approaches consist of generalized descent methods (including trajectory or tunneling methods [194, 57, 170, 182] 21 trace methods [197, 174] and local minimum penalty methods [44, 75] and learning based methods [38, 39] Generalized descent methods improve over local search methods by continuing their search process whenever a local minimum is found. There are three approaches to achieve this. First, trajectory or tunneling methods ....
....the local descent trajectory in order to escape from local minima. These methods require the di#erentiability of the objective and constraint functions, and their main disadvantage is the large number of function evaluations that are spent at unpromising regions. Second, a trace based method [197, 174] is a trajectory method that uses an external force to pull a search out of local minima and picks up good starting points from a couple of stages of global search trajectories. This method is only applicable to continuous problems with di#erentiability and may also be limited to a small search ....
Y. Shang. Global Search Methods for Solving Nonlinear Optimization Problems. Ph.D. Thesis, Dept. of Computer Science, Univ. of Illinois, Urbana, IL, August 1997.
The Theory And Applications Of Discrete Constrained Optimization.. - Wu (2000) (1 citation) (Correct)
....this thesis and point out some possible directions of future work in Chapter 7. 1.5 Significance of This Research We list in this section the main contributions of this thesis. A complete theory of discrete constrained optimization using Lagrange multipliers. Compared to previous work [207, 178, 176], we have developed a complete theory on discrete constrained optimization using Lagrange multipliers and its associated firstorder search procedure for locating CLM dn . Our proposed discrete space first order necessary and su#cient conditions can characterize all CLM dn in discrete space. In ....
Y. Shang. Global Search Methods for Solving Nonlinear Optimization Problems. Ph.D. Thesis, Dept. of Computer Science, Univ. of Illinois, Urbana, IL, August 1997.
A Lagrangian reconstruction of GENET - Choi (2000) (1 citation) (Correct)
....restrict the real variables to hold integer values only [15] Although this approach is possible, handling of the additional constraints incurs costly computation making it useless in practice. Recently Shang and Wah extended the classical Lagrange multiplier method to deal with discrete problems [11,16,17]. Consider the integer constrained minimization problem (4) 6) transformed from the CSP (U,D,C) Similar to the classical Lagrange multiplier method [9] the Lagrangian function L(#z, # #) is constructed as L(#z, # #) f(#z) # (#i,j #,#k,l#)#I # #i,j ##k,l# g #i,j ##k,l# ....
....constraints will be incorporated in the discrete gradient discussed below. A constrained minimum of the integer constrained minimization problem (4) 6) can be obtained by finding a saddle point of the Lagrangian function L(#z, # #) As in the continuous case, a saddle point (#z # , # # # ) [11,16,17] of the Lagrangian function L(#z, # #) is defined by the condition L(#z # , # #) # L(#z # , # # # ) # L(#z, # # # ) 10) for all (#z # , # #) and (#z, # # # ) sufficiently close to (#z # , # # # ) In other words, a saddle point (#z # , # # # ) of the Lagrangian function ....
[Article contains additional citation context not shown here]
Y. Shang, Global search methods for solving nonlinear optimization problems, PhD Thesis, Department of Computer Science, University of Illinois, 1997.
A Lagrangian Reconstruction of GENET - Choi, Lee, Stuckey (2000) (1 citation) (Correct)
....restrict the real variables to hold integer values only [3] Although this approach is possible, handling of the additional constraints incurs costly computation making it useless in practice. Recently Shang and Wah extended the classical Lagrange multiplier method to deal with discrete problems [38, 28, 27]. Consider the integer constrained minimization problem (4 6) transformed from the CSP (U; D;C) Similar to the classical Lagrange multiplier method [30] the Lagrangian function L( z; is constructed as L( z; f( z) X (hi;ji;hk;li)2I hi;jihk;li g hi;jihk;li ( z) 9) where z = ....
....The constraints will be incorporated in the discrete gradient discussed below. A constrained minimum of the integer constrained minimization problem (4 6) can be obtained by finding a saddle point of the Lagrangian function L( z; As in the continuous case, a saddle point ( z ; [38, 28, 27] of the Lagrangian function L( z; is defined by the condition L( z ; L( z ; L( z; 10) for all ( z ; and ( z; sufficiently close to ( z ; In other words, a saddle point ( z ; of the Lagrangian function L( z; is a minimum of L( z; ....
[Article contains additional citation context not shown here]
Y. Shang. Global Search Methods for Solving Nonlinear Optimization Problems. PhD thesis, Department of Computer Science, University of Illinois, 1997.
Efficient and Adaptive Lagrange-Multiplier Methods for Nonlinear .. - Wah, Wang (1998) (2 citations) (Correct)
....regions. Last, the trace should be designed to travel from coarse to fine so that it examines the search space in greater details when more time is allowed. Since an analytic approach to design a good trace function is intractable, we have studied some heuristic functions and fine tuned them [25]. In the following, we summarize our observations. ffl Our trace based method is a fine level global search in the sense that the search space covered by a trace grows linearly with the length of the trace (and, therefore, the time to complete the algorithm) However, a search space grows ....
Y. Shang. Global Search Methods for Solving Nonlinear Optimization Problems. Ph.D. Thesis, Dept. of Computer Science, Univ. of Illinois, Urbana, IL, August 1997.
A New Global-Search Method for Designing Filter Banks - Shang, Wah Self-citation (Shang) (Correct)
No context found.
Y. Shang. Global Search Methods for Solving Nonlinear Optimization Problems. Ph.D. Thesis, Dept. of Computer Science, Univ. of Illinois, Urbana, IL, August 1997.
Visibility Analysis and Sensor Planning in Dynamic - Environments Anurag Mittal (2004) (Correct)
No context found.
Yi Shang. Global Search Methods for Solving Nonlinear Optimization Problems. PhD thesis, University of Illinois at Urbana-Champaign, 1997.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC