Results 1  10
of
15
Continuous inverse optimal control with locally optimal examples
 In ICML
, 2012
"... Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic inverse optimal control algorithm that scales gracefully with tas ..."
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Cited by 10 (1 self)
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Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic inverse optimal control algorithm that scales gracefully with task dimensionality, and is suitable for large, continuous domains where even computing a full policy is impractical. By using a local approximation of the reward function, our method can also drop the assumption that the demonstrations are globally optimal, requiring only local optimality. This allows it to learn from examples that are unsuitable for prior methods. 1.
Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming
, 2012
"... In a recent paper, Birgin, Floudas and Martínez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the αBB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In th ..."
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Cited by 2 (0 self)
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In a recent paper, Birgin, Floudas and Martínez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the αBB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In the present research, the algorithm mentioned above will be improved in several crucial aspects. On the one hand, feasibility of the problem will not be required. Possible infeasibility will be detected in finite time by the new algorithms and optimal infeasibility results will be proved. On the other hand, finite termination results that guarantee optimality and/or feasibility up to any required precision will be provided. An adaptive modification in which subproblem tolerances depend on current feasibility and complementarity will also be given. The adaptive algorithm allows the augmented Lagrangian subproblems to be solved without requiring unnecessary potentially high precisions in the intermediate steps of the method, which improves the overall efficiency. Experiments showing how the new algorithms and results are related to practical computations will be given.
Packing ellipsoids by nonlinear optimization∗
, 2015
"... In this paper, continuous and differentiable nonlinear programming models and algorithms for packing ellipsoids in the ndimensional space are introduced. Two different models for the nonoverlapping and models for the inclusion of ellipsoids within halfspaces and ellipsoids are presented. By app ..."
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In this paper, continuous and differentiable nonlinear programming models and algorithms for packing ellipsoids in the ndimensional space are introduced. Two different models for the nonoverlapping and models for the inclusion of ellipsoids within halfspaces and ellipsoids are presented. By applying a simple multistart strategy combined with a clever choice of starting guesses and a nonlinear programming local solver, illustrative numerical experiments are presented. Key words: Cutting and packing ellipsoids, nonlinear programming, models, numerical experiments. 1
On the application of an Augmented Lagrangian algorithm to some portfolio problems ∗
, 2015
"... Algencan is a freely available piece of software that aims to solve smooth largescale constrained optimization problems. When applied to specific problems, obtaining a good performance in terms of efficacy and efficiency may depend on careful choices of options and parameters. In the present paper ..."
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Algencan is a freely available piece of software that aims to solve smooth largescale constrained optimization problems. When applied to specific problems, obtaining a good performance in terms of efficacy and efficiency may depend on careful choices of options and parameters. In the present paper the application of Algencan to four portfolio optimization problems is discussed and numerical results are presented and evaluated.
On the minimization of discontinuous functions by a smoothing method∗
, 2015
"... A general approach for the solution of some discontinuous optimization problems by means of smoothing will be proposed. It will be proved that limits of sequences generated by the suggested method satisfy a suitable optimality condition. Numerical examples will be given. Key words: discontinuous cos ..."
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A general approach for the solution of some discontinuous optimization problems by means of smoothing will be proposed. It will be proved that limits of sequences generated by the suggested method satisfy a suitable optimality condition. Numerical examples will be given. Key words: discontinuous cost functions, smoothing functions, minimization. 1
An innerouter nonlinear programming approach for constrained quadratic matrix model updating∗
, 2015
"... The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric secondorder finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original ..."
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The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric secondorder finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model. Taking advantage of the special structure of the constraint set, it is first shown that the QFEMUP can be formulated as a suitable constrained nonlinear programming problem. Using this formulation, a method based on successive optimizations is then proposed and analyzed. To avoid that spurious modes (eigenvectors) appear in the frequency range of interest (eigenvalues) after the model has been updated, additional constraints based on a quadratic Rayleigh quotient are dynamically included in the constraint set. A distinct practical feature of the proposed method is that it can be implemented by computing only a few eigenvalues and eigenvectors of the associated quadratic matrix pencil. The results of our numerical experiments on illustrative problems show that the algorithm works well in practice.
An innerouter nonlinear programming approach for constrained quadratic matrix model updating∗
, 2014
"... The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric secondorder finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original ..."
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The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric secondorder finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model. Taking advantage of the special structure of the constraint set, it is first shown that the QFEMUP can be formulated as a suitable constrained nonlinear programming problem. Using this formulation, a method based on successive optimizations is then proposed and analyzed. To avoid that spurious modes (eigenvectors) appear in the frequency range of interest (eigenvalues) after the model has been updated, additional constraints based on a quadratic Rayleigh quotient are dynamically included in the constraint set. A distinct practical feature of the proposed method is that it is implementable computing only a few eigenvalues and eigenvectors of the associated quadratic matrix pencil. The results of our numerical experiments on illustrative problems show that the algorithm works well in practice.
Invited “Discussion Paper ” for TOP CRITICAL LAGRANGE MULTIPLIERS: WHAT WE CURRENTLY KNOW ABOUT THEM, HOW THEY SPOIL OUR LIFE, AND WHAT WE CAN DO ABOUT IT∗
, 2014
"... We discuss a certain special subset of Lagrange multipliers, called critical, which usually exist when multipliers associated to a given solution are not unique. This kind of multipliers appear to be important for a number of reasons, some understood better, some (currently) not fully. What is clear ..."
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We discuss a certain special subset of Lagrange multipliers, called critical, which usually exist when multipliers associated to a given solution are not unique. This kind of multipliers appear to be important for a number of reasons, some understood better, some (currently) not fully. What is clear, is that Newton and Newtonrelated methods have an amazingly strong tendency to generate sequences with dual components converging to critical multipliers. This is quite striking because, typically, the set of critical multipliers is “thin ” (the set of noncritical ones is relatively open and dense, meaning that its closure is the whole set). Apart from mathematical curiosity to understand the phenomenon for something as classical as the Newton method, the attraction to critical multipliers is relevant computationally. This is because convergence to such multipliers is the reason for slow convergence of the Newton method in degenerate cases, as convergence to noncritical limits (if it were to happen) would have given the superlinear rate. Moreover, the attraction phenomenon shows up not only for the basic Newton method, but also for other related techniques (for example, quasiNewton, and the linearlyconstrained augmented Lagrangian method). In spite of clear computational
COMBINING STABILIZED SQP WITH THE AUGMENTED LAGRANGIAN ALGORITHM∗
, 2014
"... For an optimization problem with general equality and inequality constraints, we propose an algorithm which uses subproblems of the stabilized SQP (sSQP) type for approximately solving subproblems of the augmented Lagrangian method. The motivation is to take advantage of the wellknown robust behav ..."
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For an optimization problem with general equality and inequality constraints, we propose an algorithm which uses subproblems of the stabilized SQP (sSQP) type for approximately solving subproblems of the augmented Lagrangian method. The motivation is to take advantage of the wellknown robust behavior of the augmented Lagrangian algorithm, including on problems with degenerate constraints, and at the same time try to reduce the overall algorithm locally to sSQP (which gives fast local convergence rate under weak assumptions). Specifically, the algorithm first verifies whether the primaldual sSQP step (with unit stepsize) makes good progress towards decreasing the violation of optimality conditions for the original problem, and if so, makes this step. Otherwise, the primal part of the sSQP direction is used for linesearch that decreases the augmented Lagrangian, keeping the multiplier estimate fixed for the time being. The overall algorithm has reasonable global convergence guarantees, and inherits strong convergence rate properties of sSQP under the same weak assumptions. Numerical results on degenerate problems and comparisons with some alternatives are reported. Key words: stabilized sequential quadratic programming; augmented Lagrangian; superlinear convergence; global convergence.