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1999•ANZIAM JournalOpen access

Approximate Hessian matrices and second-order optimality conditions for nonlinear programming problems with C1-data

V. Jeyakumar, X. Wang

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Abstract

Abstract In this paper, we present generalizations of the Jacobian matrix and the Hessian matrix to continuous maps and continuously differentiable functions respectively. We then establish second-order optimality conditions for mathematical programming problems with continuously differentiable functions. The results also sharpen the corresponding results for problems involving C1.1-functions.

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Abstract In this paper, we present generalizations of the Jacobian matrix and the Hessian matrix to continuous maps and continuously differentiable functions respectively. We then establish second-order optimality conditions for mathematical programming problems with continuously differentiable functions. The results also sharpen the corresponding results for problems involving C1.1-functions.

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Available abstract

Abstract In this paper, we present generalizations of the Jacobian matrix and the Hessian matrix to continuous maps and continuously differentiable functions respectively. We then establish second-order optimality conditions for mathematical programming problems with continuously differentiable functions. The results also sharpen the corresponding results for problems involving C1.1-functions.

Key concepts: Hessian matrix, Differentiable function, Jacobian matrix and determinant, Nonlinear programming, Hessian equation, Mathematics, Order (exchange), Matrix (chemical analysis)

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