This paper concerns nonlinear semideenite programming problems for which no convexity assumptions can be made. We derive rst-and second-order op-timality conditions analogous to those for nonlinear programming. Using techniques analogous to those used in nonlinear programming, we extend existing theory to cover situations where strict complementarity does not hold and the constraint matrix is s...

This paper uses optimization theory to address a fundamental question of ethics: how to divide resources justly among individuals, groups, or organizations. It formulates utilitarian and Rawlsian criteria for distributive justice as optimization problems. The formulations recognize that some recipients are more productive than others, so that an inequitable distribution may create greater overa...

In this paper, we give necessary and suucient optimality conditions which are easy veriied for the local solution of Celis-Dennis-Tapia sub-problem (CDT subproblem) where the Hessian at this local solution has one negative eigenvalue. If CDT subproblem has no global solution with Hessian of Lagrangian positive semi-deenite, the Hessian of Lagrangian has at least one negative eigenvalue. It is v...