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The fundamental relations between geometric programming duality, parametric programming duality, and ordinary Lagrangian duality

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ANNALS OF OPERATIONS RESEARCH 2001年第1-4期105卷 109-153页

作者： Peterson, EL N Carolina State Univ Dept Math Raleigh NC 27695 USA N Carolina State Univ Grad Program Operat Res Raleigh NC 27695 USA

Every formulation of mathematical programming duality (known to the author) for continuous finite-dimensional optimization can easily be viewed as a special case of at least one of the following three formulations: the geometric programining formulation (of the generalized geometric programming type), the parametric programming formulation (of the generalized Rockafellar-perturbation type), and the ordinary Lagrangian formulation (of the generalized Falk type). The relative strengths and weaknesses of these three duality formulations are described herein, as are the fundamental relations between them. As a theoretical application, the basic duality between Fenchel's hypothesis and the existence of recession directions in convex programming is established and then expressed within each of these three duality formulations.

关键词： geometric programming ordinary programming parametric programming Lagrange multipliers post-optimality analysis conjugate transformation Legendre transformation dual cones orthogonal complementary subspaces duality theory orthogonal projection optimization convex optimization recession directions separable optimization sub-optimization

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Robust model-based tracking control using parametric programming

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COMPUTERS & CHEMICAL ENGINEERING 2004年第1-2期28卷 195-207页

作者： Sakizlis, V Dua, V Perkins, JD Pistikopoulos, EN Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2BY England

In this work, a method is presented for obtaining the explicit robust model-based tracking control law for constrained dynamic systems. The proposed control scheme guarantees optimal and feasible operation under the presence of unknown bounded input uncertainties by introducing in the controller design stage a set of feasibility constraints and employing an estimation scheme for ensuring robust offset free output tracking. The controller features a simple structure that is derived off-line via parametric programming prior to any process implementation. (C) 2002 Elsevier Ltd. All rights reserved.

关键词： model-based control robust control feasibility analysis observer design parametric programming

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Robust model-based tracking control using parametric programming

Robust model-based tracking control using parametric program...

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12th European Symposium on Computer Aided Process Engineering (ESCAPE-12)

作者： Sakizlis, V Dua, V Perkins, JD Pistikopoulos, EN Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2BY England

关键词： model-based control robust control feasibility analysis observer design parametric programming

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The explicit model-based control law for continuous time systems via parametric programming - INV5105

The explicit model-based control law for continuous time sys...

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20th Annual American Control Conference (ACC)

作者： Sakizlis, V Dua, V Perkins, JD Pistikopoulos, EN

ISBN: (纸本)0780372980

In this paper an algorithmic framework is presented for the derivation of the explicit optimal control policy for continuous linear dynamic systems that involve constraints on process inputs and outputs. The control actions are usually computed by solving regularly an on-line optimization problem in the discrete space based on a set of measurements that specify the current process state. The novel approach presented in this paper derives the optimal control law off-line as a function of the state of the process in the continuous time-domain, thus eliminating the repetitive solution of on-line optimization problems. Hence, the on-line implementation is reduced to a sequence of simple function evaluations. The key advantageous features of the algorithm are demonstrated via an illustrative example.

关键词： Calculus of variations Dynamic optimization Model predictive control parametric programming Process control Quadratic programming

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The explicit control law for hybrid systems via parametric programming

The explicit control law for hybrid systems via parametric p...

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20th Annual American Control Conference (ACC)

作者： Sakizlis, V Dua, V Perkins, JD Pistikopoulos, EN

ISBN: (纸本)0780372980

In this paper an algorithm is presented for the derivation of the explicit optimal control policy for linear dynamical systems that also involve (i) logical. decisions and (ii) constraints on process inputs and outputs. The control actions axe usually computed by solving at regular time intervals an on-line optimization problem based on a set of measurements that specify the current process state. The approach presented in this paper derives the optimal control law off-line as a function of the state of the process, thus eliminating the repetitive solution of on-line optimization problems. Hence, the on-line implementation is reduced. to a sequence of simple function evaluations. The key advantageous features of the algorithm axe demonstrated via an illustrative example.

关键词： hybrid constraint control model predictive control parametric programming mixed integer optimization

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Dynamic optimization of first-order systems via static parametric programming: application to electrical discharge machining

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JOURNAL OF MATERIALS PROCESSING TECHNOLOGY 2004年第1-3期149卷 94-98页

作者： Huguenin, P Srinivasan, B Altpeter, F Longchamp, R Ecole Polytech Fed Lausanne Lab Automat CH-1015 Lausanne Switzerland Charmilles Technol SA Appl Res CH-1217 Meyrin Switzerland

In this paper, it is shown that dynamic optimization problems of first-order systems can be transformed into a static parametric programming problem, where the state plays the role of the parameter. Thus, an optimal feedback law is obtained. This concept is applied to the die-sinking electrical discharge machining, a highly time varying industrial process which necessitates adaptation of machining settings during operation. It is shown that the minimum-time operation of this process is equivalent to choosing the manipulated variables that maximizes the speed of machining at every position. (C) 2004 Elsevier B.V. All rights reserved.

关键词： dynamic optimization first-order system electrical discharge machining parametric programming

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A Simplex Based parametric programming Method for the Large Linear programming Problem

A Simplex Based Parametric Programming Method for the Large ...

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International MultiConference of Engineers and Computer Scientists (IMECS 2012)

作者： Huang, Rujun Lou, Xinyuan South West jiaotang Univ Chengdu Si Chuan Peoples R China

ISBN: (纸本)9789881925190

We present a methodology of parametric objective function coefficient programming for large linear programming (LP) problem. Most of current parametric programming methodologies are based on the assumption that the optimal solution is available. Large linear programming problems in real-world might have millions of variables and constraints, which makes it difficult for the LP solver to return the optimal solutions. This paper extends the traditional parametric programming methodology by considering features of the large LP problems. By considering the tolerance of infeasibility and introducing a step size to deal with degeneracy of the problem, the parametric objective function coefficient linear programming of large LP problem can be conducted while the optimal solutions are not available. Experiment results of LP problems with different scales are provided.

关键词： linear programming large problem simplex-based parametric programming

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Bounded p values in parametric programming-based selective inference

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JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE 2024年第2期7卷 633-665页

作者： Shiraishi, Tomohiro Miwa, Daiki Duy, Vo Nguyen Le Takeuchi, Ichiro Nagoya Univ Nagoya 4648603 Japan Nagoya Inst Technol Nagoya 4660061 Japan Univ Informat Technol Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Vietnam RIKEN Tokyo 1030027 Japan

Selective inference (SI) has been actively studied as a promising framework for statistical hypothesis testing for data-driven hypotheses. The basic idea of SI is to make inferences conditional on an event that a hypothesis is selected. To perform SI, this event must be characterized in a traceable form. When selection event is too difficult to characterize, additional conditions are introduced for tractability. This additional conditions often cause the loss of power, and this issue is referred to as over-conditioning in Fithian et al. (Optimal inference after model selection, arXiv preprint arXiv:1410.2597, 2014). parametric programming-based SI (PP-based SI) has been proposed as one way to address the over-conditioning issue. The main problem of PP-based SI is its high computational cost due to the need to exhaustively explore the data space. In this study, we introduce a procedure to reduce the computational cost while guaranteeing the desired precision, by proposing a method to compute the lower and upper bounds of p values. We also proposed three types of search strategies that efficiently improve these bounds. We demonstrate the effectiveness of the proposed method in hypothesis testing problems for feature selection in linear models and attention region identification in deep neural networks.

关键词： Statistical hypothesis testing Selective inference parametric programming Data-driven science

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Dynamic optimization of first-order systems via static parametric programming: application to electrical discharge machining

Dynamic optimization of first-order systems via static param...

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14th International Symposium on Electromachining

作者： Huguenin, P Srinivasan, B Altpeter, F Longchamp, R Ecole Polytech Fed Lausanne Lab Automat CH-1015 Lausanne Switzerland Charmilles Technol SA Appl Res CH-1217 Meyrin Switzerland

关键词： dynamic optimization first-order system electrical discharge machining parametric programming

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Design of robust model-based tracking controllers via parametric programming

Design of robust model-based tracking controllers via parame...

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IEEE International Symposium on Computer Aided Control System Design (CACSD 2002)

作者： Sakizlis, V Kakalis, NMP Dua, V Perkins, JD Pistikopoulos, EN Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2BY England

ISBN: (纸本)078037388X

In this paper a method is presented for deriving the explicit robust model-based optimal control law for constrained linear dynamic systems. The controller underlying structure is derived off-line via parametric programming before any actual process implementation takes place. The proposed control scheme guarantees feasibility under the presence of uncertainties and disturbances, and steady state offset elimination by (i) augmenting the model dynamics with a set of integral states and (ii) explicitly incorporating in the design stage a set of feasibility constraints.

关键词： model predictive control parametric programming process control integral action robust control

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