The Experts below are selected from a list of 261 Experts worldwide ranked by ideXlab platform

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

  • Exact penalty functions method for Mathematical Programming Problems involving invex functions
    European Journal of Operational Research, 2009
    Co-Authors: Tadeusz Antczak
    Abstract:

    In this paper, some new results on the exact penalty function method are presented. Simple optimality characterizations are given for the differentiable nonconvex optimization Problems with both inequality and equality constraints via exact penalty function method. The equivalence between sets of optimal solutions in the original Mathematical Programming Problem and its associated exact penalized optimization Problem is established under suitable invexity assumption. Furthermore, the equivalence between a saddle point in the invex Mathematical Programming Problem and an optimal point in its exact penalized optimization Problem is also proved.

  • A modified objective function method in Mathematical Programming with second order invexity
    Numerical Functional Analysis and Optimization, 2007
    Co-Authors: Tadeusz Antczak
    Abstract:

    A new approach for solving nonlinear constrained Mathematical Programming Problems that makes use of second-order derivative is presented. In this method, a modified optimization Problem associated with a primal nonlinear Programming Problem is constructed that involves second-order modified objective function constituting the primal Problem. The equivalence between the nonlinear original Mathematical Programming Problem and its associated optimization Problem with a second-order modified objective function is established under second-order invexity assumption. In this way, the procedure for obtaining the second-order sufficient conditions for the Mathematical Programming Problems of this type is presented.

  • Saddle-Point Criteria in an η-Approximation Method for Nonlinear Mathematical Programming Problems Involving Invex Functions
    Journal of Optimization Theory and Applications, 2007
    Co-Authors: Tadeusz Antczak
    Abstract:

    In this paper, the η-approximation method introduced by Antczak (Ref. 1) for solving a nonlinear constrained Mathematical Programming Problem involving invex functions with respect to the same function η is extended. In this method, a so-called η-approximated optimization Problem associated with the original Mathematical Programming Problems is constructed; moreover, an η-saddle point and an η-Lagrange function are defined. By the help of the constructed η-approximated optimization Problem, saddle-point criteria are obtained for the original Mathematical Programming Problem. The equivalence between an η-saddle point of the η-Lagrangian of the associated η-approximated optimization Problem and an optimal solution in the original Mathematical Programming Problem is established.

  • An η-approximation approach to duality in Mathematical Programming Problems involving r-invex functions
    Journal of Mathematical Analysis and Applications, 2006
    Co-Authors: Tadeusz Antczak
    Abstract:

    Abstract An η -approximation approach introduced by Antczak [T. Antczak, A new method of solving nonlinear Mathematical Programming Problems involving r -invex functions, J. Math. Anal. Appl. 311 (2005) 313–323] is used to obtain a solution Mond–Weir dual Problems involving r -invex functions. η -Approximated Mond–Weir dual Problems are introduced for the η -approximated optimization Problem constructed in this method associated with the original nonlinear Mathematical Programming Problem. By the help of η -approximated dual Problems various duality results are established for the original Mathematical Programming Problem and its original Mond–Weir duals.

  • A new method of solving nonlinear Mathematical Programming Problems involving r-invex functions
    Journal of Mathematical Analysis and Applications, 2005
    Co-Authors: Tadeusz Antczak
    Abstract:

    A new approach to a solution of a nonlinear constrained Mathematical Programming Problem involving r-invex functions with respect to the same function η is introduced. An η-approximated Problem associated with an original nonlinear Mathematical Programming Problem is presented that involves η-approximated functions constituting the original Problem. The equivalence between optima points for the original Mathematical Programming Problem and its η-approximated optimization Problem is established under r-invexity assumption.

Stanisław F. Jóźwiak - One of the best experts on this subject based on the ideXlab platform.

  • Minimum weight design of structures with random parameters
    Computers & Structures, 2003
    Co-Authors: Stanisław F. Jóźwiak
    Abstract:

    Abstract A general formulation of the minimum-weight optimization Problem is presented in the paper. Formulation of the Problem is based on the concept of the expected value. Solution of the corresponding Mathematical Programming Problem has been obtained by means of indirect method. To evaluate the magnitude of the influence of random character of the structure parameters two numerical examples concerning plane truss and free vibrating plane strain structure are presented.

Shashi Kant Mishra - One of the best experts on this subject based on the ideXlab platform.

Ho Thuc Quyen - One of the best experts on this subject based on the ideXlab platform.

  • optimality conditions under relaxed quasiconvexity assumptions using star and adjusted subdifferentials
    European Journal of Operational Research, 2011
    Co-Authors: Phan Quoc Khanh, Ho Thuc Quyen
    Abstract:

    A set-constrained optimization Problem and a Mathematical Programming Problem are considered. We assume that the sublevel sets of the involving functions are convex only at the point under question and hence these functions are not assumed quasiconvex. Using the two star subdifferentials and the adjusted subdifferential, we establish optimality conditions for usual minima and strict minima. Our results contain and improve some recent ones in the literature. Examples are provided to explain the advantages of each of our results.

Mahendra Prasad Biswal - One of the best experts on this subject based on the ideXlab platform.

  • Linear fractional Programming Problems with some multi-choice parameters
    International Journal of Operational Research, 2019
    Co-Authors: Avik Pradhan, Mahendra Prasad Biswal
    Abstract:

    Linear fractional Programming is a class of Mathematical Programming Problem where we optimise the ratio of two linear functions subject to some linear constraints. In this paper, we present a linear fractional Programming model where some or all the parameters are multi-choice type. We present a novel and efficient method, which integrates classical Charnes-Cooper transformation and Lagrange's interpolating polynomial, to transform multi-choice linear fractional Programming Problems into an equivalent mixed-integer nonlinear Programming (MINLP) Problems. A theorem is presented to establish the relation between the optimal solution of the multi-choice linear fractional programs and the equivalent MINLP. Some numerical examples are studied to illustrate the methodology.

  • Probabilistic linear Programming Problems with exponential random variables: A technical note
    European Journal of Operational Research, 1998
    Co-Authors: Mahendra Prasad Biswal, N.p. Biswal
    Abstract:

    A method for solving probabilistic linear Programming Problems with exponential random variables is presented in this paper. Assuming that either some or all of the parameters are exponential random variables a transformation is presented to convert the probabilistic linear Programming Problem to a deterministic Mathematical Programming Problem. A non-linear Programming algorithm can then be used to solve the resulting deterministic Problem.