The theory of self-scaled conic programming provides a uniied framework for the theories of linear programming, semideenite programming and convex quadratic programming with convex quadratic constraints. Nesterov and Todd's concept of self-scaled barrier functionals allows the exploitation of algebraic and geometric properties of symmetric cones in certain variants of the barrier method applied...

This paper considers a special but broad class of convex programming (CP) problems whose feasible region is a simple compact convex set intersected with the inverse image of a closed convex cone under an affine transformation. It studies the computational complexity of quadratic penalty based methods for solving the above class of problems. An iteration of these methods, which is simply an iter...

We discuss two facets of the interaction between geometry and algebra in Banach algebras. In class unital algebras, there is essentially one known example which also strictly convex as a space. recall this example, finite-dimensional, consider open question generalising it to infinite dimensions. C*-algebras, we exhibit striking tighter relationship that exists there.

This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and non-convex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the lift-a...

Second-order cone programming (SOCP) problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the Cartesian product of second-order (Lorentz) cones. Linear programs, convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as SOCP problems, as can many other problems t...

The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadratic programming, semide nite programming, and nonconvex and nonlinear problems, have reached varyin...

A new Neumann-Neumann type domain decomposition algorithm for the solution of contact problems of elasticity and similar problems is described. The discretized variational inequality that models the equilibrium of a system of elastic bodies in contact is first turned by duality to a strictly convex quadratic programming problem with either box constraints or box and equality constraints. This s...

The underestimation of data points by a convex quadratic function is a useful tool for approximating the location of the global minima of potential energy functions that arise in protein-ligand docking problems. Determining the parameters that define the underestimator can be formulated as a convex quadratically constrained quadratic program and solved efficiently using algorithms for semidefin...