scholarly journals A Fritz John type sufficient optimality theorem in complex space

1974 ◽  
Vol 11 (2) ◽  
pp. 219-224 ◽  
Author(s):  
T.R. Gulati
Keyword(s):  
Nonlinear Programming ◽  
Complex Space ◽  
Inequality Constraints ◽  
Polyhedral Cones ◽  
Finite Dimensional

A Fritz John type sufficient optimality theorem is proved for nonlinear programming problems in finite dimensional complex space over polyhedral cones, which may include equality as well as inequality constraints.

scholarly journals A Fritz John theorem in complex space

1973 ◽  
Vol 8 (2) ◽  
pp. 215-220 ◽  
Author(s):  
B.D. Craven ◽  
B. Mond
Keyword(s):  
Nonlinear Programming ◽  
Complex Space ◽  
Necessary Conditions ◽  
Polyhedral Cone ◽  
Necessary Condition ◽  
Feasible Point ◽  
Polyhedral Cones ◽  
Differentiable Functions ◽  
Finite Dimensional ◽  
Image Position

Necessary conditions of the Fritz John type are given for a class of nonlinear programming problems over polyhedral cones in finite dimensional complex space.Consider the problem towhere S is a polyhedral cone in, and Cm and f: C2n → C, g : C2n → Cm are differentiable functions. A necessary condition for a feasible point z0 to be optimal is that there exist τ≥0, ν ∈ S*, (τ, ν) ≠ 0, such thatand

Sufficient Fritz John optimality conditions

1975 ◽  
Vol 13 (3) ◽  
pp. 411-419 ◽  
Author(s):  
B.D. Craven
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Linear Subspace ◽  
Arbitrary Dimension ◽  
Differentiable Manifold ◽  
The Other ◽  
Sufficient Optimality Conditions ◽  
Polyhedral Cones ◽  
Finite Dimensional ◽  
Fritz John Optimality Conditions

The sufficient optimality conditions, of Fritz John type, given by Gulati for finite-dimensional nonlinear programming problems involving polyhedral cones, are extended to problems with arbitrary cones and spaces of arbitrary dimension, whether real or complex. Convexity restrictions on the function giving the equality constraint can be avoided by applying a modified notion of convexity to the other functions in the problem. This approach regards the problem as optimizing on a differentiable manifold, and transforms the problem to a locally equivalent one where the optimization is on a linear subspace.

scholarly journals On converse duality in complex nonlinear programming

1975 ◽  
Vol 13 (3) ◽  
pp. 421-427 ◽  
Author(s):  
J. Parida
Keyword(s):  
Nonlinear Programming ◽  
Duality Theorem ◽  
Complex Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Converse Duality ◽  
Finite Dimensional ◽  
Necessary And Sufficient ◽  
Direct Use ◽  
Converse Duality Theorem

In this note a converse duality theorem is proved for a class of nonlinear programming problems over polyhedral cones in finite dimensional complex space by a direct use of a Kuhn-Tucker type necessary and sufficient condition for constrained optimization in complex space.

On an application of the complex nonlinear complementarity problem

1976 ◽  
Vol 15 (1) ◽  
pp. 141-148 ◽  
Author(s):  
J. Parida ◽  
B. Sahoo
Keyword(s):  
Minimization Problem ◽  
Complementarity Problem ◽  
Complex Space ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Polyhedral Cones ◽  
Existence Of A Solution ◽  
Nonlinear Complementarity

A theorem on the existence of a solution under feasibility assumptions to a convex minimization problem over polyhedral cones in complex space is given by using the fact that the problem of solving a convex minimization program naturally leads to the consideration of the following nonlinear complementarity problem: given g: Cn → Cn, find z such that g(z) ∈ S*, z ∈ S, and Re〈g(z), z〉 = 0, where S is a polyhedral cone and S* its polar.

A Class of Augumented Lagrangian Function for Nonlinear Programming

2011 ◽  
Vol 271-273 ◽  
pp. 1955-1960
Author(s):  
Mei Xia Li
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Inequality Constraints ◽  
Unconstrained Minimization ◽  
Lagrangian Function ◽  
Point Of View ◽  
Theoretical Point ◽  
Non Linear Programming ◽  
Global Minimizers ◽  
Equality And Inequality Constraints

In this paper, we discuss an exact augumented Lagrangian functions for the non- linear programming problem with both equality and inequality constraints, which is the gen- eration of the augmented Lagrangian function in corresponding reference only for inequality constraints nonlinear programming problem. Under suitable hypotheses, we give the relation- ship between the local and global unconstrained minimizers of the augumented Lagrangian function and the local and global minimizers of the original constrained problem. From the theoretical point of view, the optimality solution of the nonlinear programming with both equality and inequality constraints and the values of the corresponding Lagrangian multipli- ers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augumented Lagrangian function presented in this paper.

scholarly journals Mixed-type duality for multiobjective fractional variational control problems

2005 ◽  
Vol 2005 (1) ◽  
pp. 109-124 ◽  
Author(s):  
Raman Patel
Keyword(s):  
Nonlinear Programming ◽  
Convex Functions ◽  
Mixed Type ◽  
Efficient Solutions ◽  
Control Problems ◽  
Duality Results ◽  
Finite Dimensional ◽  
Duality Relations ◽  
Mixed Type Duality ◽  
Convexity Assumptions

The concept of mixed-type duality has been extended to the class of multiobjective fractional variational control problems. A number of duality relations are proved to relate the efficient solutions of the primal and its mixed-type dual problems. The results are obtained forρ-convex (generalizedρ-convex) functions. The results generalize a number of duality results previously obtained for finite-dimensional nonlinear programming problems under various convexity assumptions.

scholarly journals Duality in finite dimensional complex space

1978 ◽  
Vol 18 (1) ◽  
pp. 65-75
Author(s):  
C.H. Scott ◽  
T.R. Jefferson
Keyword(s):  
Quadratic Programming ◽  
Duality Theory ◽  
Complex Space ◽  
Optimization Problems ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Mathematical Programs ◽  
Finite Dimensional ◽  
General Duality ◽  
General Duality Theory

The idea of duality is now a widely accepted and useful idea in the analysis of optimization problems posed in real finite dimensional vector spaces. Although similar ideas have filtered over to the analysis of optimization problems in complex space, these have mainly been concerned with problems of the linear and quadratic programming variety. In this paper we present a general duality theory for convex mathematical programs in finite dimensional complex space, and, by means of an example, show that this formulation captures all previous results in the area.

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