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27
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.
An SQP Algorithm For Finely Discretized Continuous Minimax Problems And Other Minimax Problems With Many Objective Functions
, 1996
"... . A common strategy for achieving global convergence in the solution of semiinfinite programming (SIP) problems, and in particular of continuous minimax problems, is to (approximately) solve a sequence of discretized problems, with a progressively finer discretization meshes. Finely discretized min ..."
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Cited by 20 (2 self)
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. A common strategy for achieving global convergence in the solution of semiinfinite programming (SIP) problems, and in particular of continuous minimax problems, is to (approximately) solve a sequence of discretized problems, with a progressively finer discretization meshes. Finely discretized minimax and SIP problems, as well as other problems with many more objectives /constraints than variables, call for algorithms in which successive search directions are computed based on a small but significant subset of the objectives/constraints, with ensuing reduced computing cost per iteration and decreased risk of numerical difficulties. In this paper, an SQPtype algorithm is proposed that incorporates this idea in the particular case of minimax problems. The general case will be considered in a separate paper. The quadratic programming subproblem that yields the search direction involves only a small subset of the objective functions. This subset is updated at each iteration in such a wa...
Computational Discretization Algorithms For Functional Inequality Constrained Optimization
, 1999
"... In this paper, a functional inequality constrained optimization problem is studied using a discretization method and an adaptive scheme. The problem is discretized by partitioning the interval of the independent parameter. Two methods are investigated as to how to treat the discretized optimization ..."
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Cited by 12 (3 self)
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In this paper, a functional inequality constrained optimization problem is studied using a discretization method and an adaptive scheme. The problem is discretized by partitioning the interval of the independent parameter. Two methods are investigated as to how to treat the discretized optimization problem. The discretization problem is firstly converted into an optimization problem with a single nonsmooth equality constraint. Since the obtained equality constraint is nonsmooth and does not satisfy the usual constraint qualification condition, relaxation and smoothing techniques are used to approximate the equality constraint via a smooth inequality constraint. This leads to a sequence of approximate smooth optimization problems with one constraint. An adaptive scheme is incorporated into the method to facilitate the computation of the sum in the inequality constraint. The second method is to apply an adaptive scheme directly to the discretization problem. Thus a sequence of optimization problems with a small number of inequality constraints are obtained. Convergence analysis for both methods is established. Numerical examples show that each of the two proposed methods has its own advantages and disadvantages over the other.
Synthesis of Manufacturable Analog Circuits
 Proceedings of ACM/IEEE ICCAD
"... Abstract † We describe a synthesis system that takes operating range constraints and inter and intra circuit parametric manufacturing variations into account while designing a sized and biased analog circuit. Previous approaches to CAD for analog circuit synthesis have concentrated on nominal anal ..."
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Cited by 10 (6 self)
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Abstract † We describe a synthesis system that takes operating range constraints and inter and intra circuit parametric manufacturing variations into account while designing a sized and biased analog circuit. Previous approaches to CAD for analog circuit synthesis have concentrated on nominal analog circuit design, and subsequent optimization of these circuits for statistical fluctuations and operating point ranges. Our approach simultaneously synthesizes and optimizes for operating and manufacturing variations by mapping the circuit design problem into an Infinite Programming problem and solving it using an annealing within annealing formulation. We present circuits designed by this integrated synthesis system, and show that they indeed meet their operating range and parametric manufacturing constraints. 1
Logarithmic Barrier Decomposition Methods for SemiInfinite Programming
, 1996
"... A computational study of some logarithmic barrier decomposition algorithms for semiinfinite programming is presented in this paper. The conceptual algorithm is a straightforward adaptation of the logarithmic barrier cutting plane algorithm which was presented recently by den Hertog et al., to solv ..."
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Cited by 9 (1 self)
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A computational study of some logarithmic barrier decomposition algorithms for semiinfinite programming is presented in this paper. The conceptual algorithm is a straightforward adaptation of the logarithmic barrier cutting plane algorithm which was presented recently by den Hertog et al., to solve semiinfinite programming problems. Usually decomposition (cutting plane methods) use cutting planes to improve the localization of the given problem. In this paper we propose an extension which uses linear cuts to solve large scale, difficult real world problems. This algorithm uses both static and (doubly) dynamic enumeration of the parameter space and allows for multiple cuts to be simultaneously added for larger/difficult problems. The algorithm is implemented both on sequential and parallel computers. Implementation issues and parallelization strategies are discussed and encouraging computational results are presented. Keywords: column generation, convex programming, cutting plane met...
Feasible Sequential Quadratic Programming For Finely Discretized Problems From Sip
, 1998
"... A Sequential Quadratic Programming algorithm designed to efficiently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from finely discretized SemiInfinite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few o ..."
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Cited by 8 (1 self)
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A Sequential Quadratic Programming algorithm designed to efficiently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from finely discretized SemiInfinite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few of the constraints are used in the QP subproblems at each iteration, and (ii) that every iterate satisfies all constraints. 1 INTRODUCTION Consider the SemiInfinite Programming (SIP) problem minimize f(x) subject to \Phi(x) 0; (SI) where f : IR n ! IR is continuously differentiable, and \Phi : IR n ! IR is defined by \Phi(x) \Delta = sup ¸2[0;1] OE(x; ¸); with OE : IR n \Theta [0; 1] ! IR continuously differentiable in the first argument. For an excellent survey of the theory behind the problem (SI), in addition to some algorithms and applications, see [9] as well as the other papers in the present volume. Many globally convergent algorithms designed to solve (SI) 2 Chapter 1...
Semismooth Newton Methods for Solving SemiInfinite Programming Problems
, 2000
"... In this paper we present some semismooth Newton methods for solving the semiinfinite programming problem. We first reformulate the first order optimality condition of the problem into a system of semismooth equations by using NCP functions. Then some semismooth Newton methods are proposed for solvi ..."
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Cited by 8 (3 self)
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In this paper we present some semismooth Newton methods for solving the semiinfinite programming problem. We first reformulate the first order optimality condition of the problem into a system of semismooth equations by using NCP functions. Then some semismooth Newton methods are proposed for solving this system of semismooth equations. Under some standard assumptions these methods are globally and superlinearly convergent. Numerical results are also given.
A new approach to fitting linear models in high dimensional spaces
, 2000
"... This thesis presents a new approach to fitting linear models, called “pace regression”, which also overcomes the dimensionality determination problem. Its optimality in minimizing the expected prediction loss is theoretically established, when the number of free parameters is infinitely large. In th ..."
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Cited by 7 (0 self)
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This thesis presents a new approach to fitting linear models, called “pace regression”, which also overcomes the dimensionality determination problem. Its optimality in minimizing the expected prediction loss is theoretically established, when the number of free parameters is infinitely large. In this sense, pace regression outperforms existing procedures for fitting linear models. Dimensionality determination, a special case of fitting linear models, turns out to be a natural byproduct. A range of simulation studies are conducted; the results support the theoretical analysis. Through the thesis, a deeper understanding is gained of the problem of fitting linear models. Many key issues are discussed. Existing procedures, namely OLS, AIC, BIC, RIC, CIC, CV(d), BS(m), RIDGE, NNGAROTTE and LASSO, are reviewed and compared, both theoretically and empirically, with the new methods. Estimating a mixing distribution is an indispensable part of pace regression. A measurebased minimum distance approach, including probability measures and nonnegative measures, is proposed, and strongly consistent estimators are produced. Of all minimum distance methods for estimating a mixing distribution, only the
An Unconstrained Convex Programming Approach to Linear SemiInfinite Programming
, 1998
"... . In this paper, an unconstrained convex programming dual approach for solving a class of linear semiinfinite programming problems is proposed. Both primal and dual convergence results are established under some basic assumptions. Numerical examples are also included to illustrate this approach. ..."
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Cited by 5 (2 self)
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. In this paper, an unconstrained convex programming dual approach for solving a class of linear semiinfinite programming problems is proposed. Both primal and dual convergence results are established under some basic assumptions. Numerical examples are also included to illustrate this approach. Key words. Semiinfinite programming, linear programming, convex programming, entropy optimization. AMS subject classifications. 90C05, 90C34, 49M35 1. Introduction. Many linear semiinfinite programming problems including the L1 and Chebychev approximation problems [14, 15] appear in the following "dual form": Program (D) Max b T w s.t. a(t) T w c(t); 8t 2 T; (1.1) where b; w 2 R m , T is a compact set in R n , a(t) T = (a 1 (t); : : : ; am (t)), and c(t) and a j (t); j = 1; : : : ; m; are continuous functions defined on T . A corresponding "primal form" linear semiinfinite programming problem can be represented as follows. Program (P ) Min Z T c(t)x(t)d(t) s.t. Z T ...