1.1. Lagrange Duality . . . . . . . . . . . . . . . . . . p. 2 1.1.1. Separable Problems – Decomposition . . . . . . . p. 7 1.1.2. Partitioning . . . . . . . . . . . . . . . . . . p. 9 1.2. Fenchel Duality and Conic Programming . . . . . . . . p. 10 1.2.1. Linear Conic Problems . . . . . . . . . . . . . p. 15 1.2.2. Second Order Cone Programming . . . . . . . . . p. 17 1.2.3. Semidefinite Progr...

Operations research, optimization, constraint programming, hybrid solution methods, decision Handbook of Semidefinite, Cone and Polynomial Optimization:. Learning Outcomes. On successful completion of this module, the student should: Have a working knowledge of the techniques employed in a modern constraint. Constraint-based scheduling: applying constraint programming to scheduling Implementati...

In this paper we present a new algorithm for solving the second order cone programming problems which we call the Q method. This algorithm is an extension of the Q method of Alizadeh Haeberly and Overton for the semidefinite programming problem.

We discuss first and second order optimality conditions for nonlinear second-order cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong regularity in terms of second order optimality conditions.

This paper proposes an infeasible interior-point algorithm with full Nesterov-Todd step for second-order cone programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110–1136, 2006). The polynomial bound coincides with that of infeasible interior-point methods for linear programming, namely, O(l log l/ε).

The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It interesting both in theory practice to investigate which admit representation using SOCs, given that they have strong expressive ability. In this paper, we prove constructively the sums nonnegative circuits (SONC) admits SOC representation. B...

Lifts/extended formulations/cone representations of convex sets currently form an active area of research in optimization, computer science, real algebraic geometry and convex geometry. We invite high quality papers on all optimization related aspects of this topic for a special issue of Mathematical Programming, Series B. All submitted papers will be refereed according to the standards of Math...

We present a quantum interior-point method (IPM) for second-order cone programming (SOCP) that runs in time $\widetilde{O} \left( n\sqrt{r} \frac{\zeta \kappa}{\delta^2} \log \left(1/\epsilon\right) \right)$ where $r$ is the rank and $n$ dimension of SOCP, $\delta$ bounds distance intermediate solutions from boundary, $\zeta$ parameter upper bounded by $\sqrt{n}$, $\kappa$ an bound on condition...

minimize cx such that Ax = b and x ∈ Λ+, where c ∈ R, Ax = b is a system of linear equations and Λ+ is the closure of a so called hyperbolicity cone. Hyperbolic programming generalizes semidefinite programming, but it is not known to what extent since it is not known how general the hyperbolicity cones are. The rich algebraic structure of hyperbolicity cones makes hyperbolic programming an inte...