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41
On Combining Feasibility, Descent and Superlinear Convergence in Inequality Constrained Optimization
 Mathematical Programming
, 1993
"... . Extension of quasiNewton techniques from unconstrained to constrained optimization via Sequential Quadratic Programming (SQP) presents several difficulties. Among these are the possible inconsistency, away from the solution, of first order approximations to the constraints, resulting in infeasibi ..."
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Cited by 60 (2 self)
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. Extension of quasiNewton techniques from unconstrained to constrained optimization via Sequential Quadratic Programming (SQP) presents several difficulties. Among these are the possible inconsistency, away from the solution, of first order approximations to the constraints, resulting in infeasibility of the quadratic programs; and the task of selecting a suitable merit function, to induce global convergence. In the case of inequality constrained optimization, both of these difficulties disappear if the algorithm is forced to generate iterates that all satisfy the constraints, and that yield monotonically decreasing objective function values. (Feasibility of the successive iterates is in fact required in many contexts such as in realtime applications or when the objective function is not well defined outside the feasible set). It has been recently shown that this can be achieved while preserving local twostep superlinear convergence. In this note, the essential ingredients for an S...
A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm
 SIAM Journal on Optimization
, 2001
"... . A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the pr ..."
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Cited by 56 (0 self)
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. A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the proposed scheme still enjoys the same global and fast local convergence properties. A preliminary implementation has been tested and some promising numerical results are reported. Key words. sequential quadratic programming, SQP, feasible iterates, feasible SQP, FSQP AMS subject classifications. 49M37, 65K05, 65K10, 90C30, 90C53 PII. S1052623498344562 1.
On the constant positive linear dependence condition and its application to SQP methods
 SIAM Journal on Optimization
, 2000
"... Abstract. In this paper, we introduce a constant positive linear dependence condition (CPLD), which is weaker than the Mangasarian–Fromovitz constraint qualification (MFCQ) and the constant rank constraint qualification (CRCQ). We show that a limit point of a sequence of approximating Karush–Kuhn–Tu ..."
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Cited by 50 (3 self)
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Abstract. In this paper, we introduce a constant positive linear dependence condition (CPLD), which is weaker than the Mangasarian–Fromovitz constraint qualification (MFCQ) and the constant rank constraint qualification (CRCQ). We show that a limit point of a sequence of approximating Karush–Kuhn–Tucker (KKT) points is a KKT point if the CPLD holds there. We show that a KKT point satisfying the CPLD and the strong secondorder sufficiency conditions (SSOSC) is an isolated KKT point. We then establish convergence of a general sequential quadratical programming (SQP) method under the CPLD and the SSOSC. Finally, we apply these results to analyze the feasible SQP method proposed by Panier and Tits in 1993 for inequality constrained optimization problems. We establish its global convergence under the SSOSC and a condition slightly weaker than the Mangasarian–Fromovitz constraint qualification, and we prove superlinear convergence of a modified version of this algorithm under the SSOSC and a condition slightly weaker than the linear independence constraint qualification.
Global Search Methods For Solving Nonlinear Optimization Problems
, 1997
"... ... these new methods, we develop a prototype, called Novel (Nonlinear Optimization Via External Lead), that solves nonlinear constrained and unconstrained problems in a unified framework. We show experimental results in applying Novel to solve nonlinear optimization problems, including (a) the lear ..."
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Cited by 18 (1 self)
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... these new methods, we develop a prototype, called Novel (Nonlinear Optimization Via External Lead), that solves nonlinear constrained and unconstrained problems in a unified framework. We show experimental results in applying Novel to solve nonlinear optimization problems, including (a) the learning of feedforward neural networks, (b) the design of quadraturemirrorfilter digital filter banks, (c) the satisfiability problem, (d) the maximum satisfiability problem, and (e) the design of multiplierless quadraturemirrorfilter digital filter banks. Our method achieves better solutions than existing methods, or achieves solutions of the same quality but at a lower cost.
Global Optimization For Constrained Nonlinear Programming
, 2001
"... In this thesis, we develop constrained simulated annealing (CSA), a global optimization algorithm that asymptotically converges to constrained global minima (CGM dn ) with probability one, for solving discrete constrained nonlinear programming problems (NLPs). The algorithm is based on the necessary ..."
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Cited by 14 (2 self)
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In this thesis, we develop constrained simulated annealing (CSA), a global optimization algorithm that asymptotically converges to constrained global minima (CGM dn ) with probability one, for solving discrete constrained nonlinear programming problems (NLPs). The algorithm is based on the necessary and sufficient condition for constrained local minima (CLM dn ) in the theory of discrete constrained optimization using Lagrange multipliers developed in our group. The theory proves the equivalence between the set of discrete saddle points and the set of CLM dn, leading to the firstorder necessary and sufficient condition for CLM dn. To find
BIOINFORMATICS ORIGINAL PAPER
"... doi:10.1093/bioinformatics/btl190 Independent component analysisbased penalized discriminant method for tumor classification using gene expression data ..."
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Cited by 9 (2 self)
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doi:10.1093/bioinformatics/btl190 Independent component analysisbased penalized discriminant method for tumor classification using gene expression data
A sequential quadratically constrained quadratic programming method for . . .
 JOURNAL OF MATHEMATICAL ANALYSIS AND
, 2010
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A superlinearly convergent strongly subfeasible SSLEtype algorithm with working set for . . .
 JOURNAL OF COMPUTATIONAL AND APPLIED
, 2009
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Methods for nonlinear constraints in optimization calculations
 THE STATE OF THE ART IN NUMERICAL ANALYSIS
, 1996
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