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T. Antczak - One of the best experts on this subject based on the ideXlab platform.

  • Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems
    Journal of Optimization Theory and Applications, 2018
    Co-Authors: T. Antczak
    Abstract:

    In the paper, the classical exact absolute value Function Method is used for solving a nondifferentiable constrained interval-valued optimization problem with both inequality and equality constraints. The property of exactness of the penalization for the exact absolute value Penalty Function Method is analyzed under assumption that the Functions constituting the considered nondifferentiable constrained optimization problem with the interval-valued objective Function are convex. The conditions guaranteeing the equivalence of the sets of LU-optimal solutions for the original constrained interval-valued extremum problem and for its associated penalized optimization problem with the interval-valued exact absolute value Penalty Function are given.

  • the exactness property of the vector exact l1 Penalty Function Method in nondifferentiable invex multiobjective programming
    Numerical Functional Analysis and Optimization, 2016
    Co-Authors: T. Antczak, Marcin Studniarski
    Abstract:

    ABSTRACTIn this article, the vector exact l1 Penalty Function Method used for solving nonconvex nondifferentiable multiobjective programming problems is analyzed. In this Method, the vector penalized optimization problem with the vector exact l1 Penalty Function is defined. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penalized optimization problem with the vector exact l1 Penalty Function. This equivalence is established for nondifferentiable invex vector optimization problems. Some examples of vector optimization problems are presented to illustrate the results established in the article.

  • vector exponential Penalty Function Method for nondifferentiable multiobjective programming problems
    Bulletin of the Malaysian Mathematical Sciences Society, 2016
    Co-Authors: T. Antczak
    Abstract:

    In this paper, a new vector exponential Penalty Function Method for nondifferentiable multiobjective programming problems with inequality constraints is introduced. First, the case when a sequence of vector penalized optimization problems with vector exponential Penalty Function constructed for the original multiobjective programming problem is considered, and the convergence of this Method is established. Further, the exactness property of a vector exact Penalty Function Method is defined and analyzed in the context of the introduced vector exponential Penalty Function Method. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto solutions of the considered nondifferentiable multiobjective programming problem and the associated vector penalized optimization problem with the vector exact exponential Penalty Function. This equivalence is established for nondifferentiable vector optimization problems with inequality constraints in which involving Functions are r-invex.

  • The exact absolute value Penalty Function Method for identifying strict global minima of order m in nonconvex nonsmooth programming
    Optimization Letters, 2015
    Co-Authors: T. Antczak
    Abstract:

    In this paper, it is demonstrated that the exact absolute value Penalty Function Method is useful for identifying the special sort of minimizers in nonconvex nonsmooth optimization problems with both inequality and equality constraints. The equivalence between the sets of strict global minima of order m in nonsmooth minimization problem and of its associated penalized optimization problem with the exact \(l_{1}\) Penalty Function is established under nondifferentiable \(\left( F,\rho \right) \)-convexity assumptions imposed on the involved Functions. The threshold of the Penalty parameter, above which this result holds, is also given.

  • Exactness of penalization for exact minimax Penalty Function Method in nonconvex programming
    Applied Mathematics and Mechanics, 2015
    Co-Authors: T. Antczak
    Abstract:

    The exact minimax Penalty Function Method is used to solve a nonconvex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax Penalty Function Method are established by assuming that the Functions constituting the considered constrained optimization problem are invex with respect to the same Function η (with the exception of those equality constraints for which the associated Lagrange multipliers are negative—these Functions should be assumed to be incave with respect to η). Thus, a threshold of the Penalty parameter is given such that, for all Penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax Penalty Function. It is shown that coercivity is not sufficient to prove the results.

Anurag Jayswal - One of the best experts on this subject based on the ideXlab platform.

Sarita Choudhury - One of the best experts on this subject based on the ideXlab platform.

Toshiyuki Ohtsuka - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear model predictive control for systems with state dependent switches and state jumps using a Penalty Function Method
    2018 IEEE Conference on Control Technology and Applications (CCTA), 2018
    Co-Authors: Sotaro Katayama, Yasuyuki Satoh, Masahiro Doi, Toshiyuki Ohtsuka
    Abstract:

    In this work, we propose a real-time algorithm of nonlinear model predictive control (NMPC) for a class of switched systems with state-dependent switches and state jumps based on the continuation/GMRES (C/GMRES) Method. This approach utilizes the characteristic of NMPC that the optimal solution changes continuously with respect to time and optimizes control input and switching instants simultaneously by updating them at each sampling time. To avoid difficulty in updating the solution based on the C/GMRES Method and to construct a simple algorithm, we treat the switching condition by using a Penalty Function Method. We demonstrate the effectiveness of the proposed Method using a numerical simulation of a compass-like biped walking robot, which contains state-dependent discrete events.

  • nonlinear model predictive control for systems with autonomous state jumps using a Penalty Function Method
    Asian Control Conference, 2017
    Co-Authors: Sotaro Katayama, Yasuyuki Satoh, Masahiro Doi, Toshiyuki Ohtsuka
    Abstract:

    In this paper, we propose a real-time algorithm of nonlinear model predictive control for systems with state jumps based on the C/GMRES Method. Applying a standard numerical solution Method directly to an optimal control problem with state jumps is generally difficult because of additional constraints associated with the state jumps. We introduce a Penalty Function Method to avoid these difficulties. We demonstrate the effectiveness of the proposed Method using a numerical simulation of a compass-like biped walking robot.

Yantao Wang - One of the best experts on this subject based on the ideXlab platform.

  • A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints
    Abstract and Applied Analysis, 2014
    Co-Authors: Xiangyu Gao, Xian Zhang, Yantao Wang
    Abstract:

    We consider an optimal control problem subject to the terminal state equality constraint and continuous inequality constraints on the control and the state. By using the control parametrization Method used in conjunction with a time scaling transform, the constrained optimal control problem is approximated by an optimal parameter selection problem with the terminal state equality constraint and continuous inequality constraints on the control and the state. On this basis, a simple exact Penalty Function Method is used to transform the constrained optimal parameter selection problem into a sequence of approximate unconstrained optimal control problems. It is shown that, if the Penalty parameter is sufficiently large, the locally optimal solutions of these approximate unconstrained optimal control problems converge to the solution of the original optimal control problem. Finally, numerical simulations on two examples demonstrate the effectiveness of the proposed Method.