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16 - Multiobjective Optimization
from Part III - Formulation and Solution of Linear Programming (LP) Problems
Vassilios S. Vassiliadis, University of Cambridge, Walter Kähm, Ehecatl Antonio del Rio Chanona, Imperial College London, Ye Yuan
Book:

Optimization for Chemical and Biochemical Engineering

Published online:

17 December 2020

Print publication:

14 January 2021, pp 168-194
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Summary

Non-differentiable optimization is a topic of contemporary interest in several applications.Non-differentiability may arise from piecewise descriptions of the objective function or the constraints, and requires special handling in order to derive solutions for such problems.Here in this chapter the emphasis is given on subgradient methods, with a basic introduction on subdifferentials and all associated necessary concepts.

Corrigendum to: Dirichlet and Neumann boundary conditions for the p-Laplace operator: What is in between?
Part of
Ralph Chill, Mahamadi Warma
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 6 / December 2019

Published online by Cambridge University Press:

01 February 2019, pp. 1689-1691

Print publication:

December 2019
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The implication $(i)\Rightarrow (ii)$ of Theorem 2.1 in our article [1] is not true as it stands. We give here two correct statements which follow from the original proof.

Extremal characterizations of reflexive spaces
Part of
- Existence theories
Xianfu Wang
Journal:

Journal of the Australian Mathematical Society / Volume 82 / Issue 3 / June 2007

Published online by Cambridge University Press:

09 April 2009, pp. 429-440

Print publication:

June 2007
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Assume that a Banach space has a Fréchet differentiable and locally uniformly convex norm. We show that the reflexive property of the Banach space is not only sufficient, but also a necessary condition for the fulfillment of the proximal extremal principle in nonsmooth analysis.

Characterization of optimality for the abstract convex program with finite dimensional range
Jon M. Borwein
Journal:

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 30 / Issue 4 / April 1981

Published online by Cambridge University Press:

09 April 2009, pp. 390-411

Print publication:

April 1981
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This paper presents characterizations of optimality for the abstract convex program
when S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S-convex (on Ω). These characterizations, which include a Lagrange multiplier theorem and do not presume any a priori constraint qualification, subsume those presently in the literature.

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