Circular programming problems are a new class of convex optimization problems in which we minimize linear function over the intersection of an affine linear manifold with the Cartesian product of circular cones. It has very recently been discovered that, unlike what has previously been believed, circular programming is a special case of symmetric programming, where it lies between second-order ...

We consider symmetrized KKT systems arising in the solution of convex quadratic programming problems in standard form by Interior Point methods. Their coefficient matrices usually have 3×3 block structure and, under suitable conditions on both the quadratic programming problem and the solution, they are nonsingular in the limit. We present new spectral estimates for these matrices: the new boun...

This paper addresses the globally optimal solution of the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network. We formulate the NCUC as a mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. A global optimization algorithm is developed based on a multi-tree approach that iterates betwe...

Copositive optimization is a quickly expanding scientific research domain with wide-spread applications ranging from global nonconvex problems in engineering to NP-hard combinatorial optimization. It falls into the category of conic programming (optimizing a linear functional over a convex cone subject to linear constraints), namely the cone C of all completely positive symmetric n×n matrices (...

The low-rank solutions of continuous and discrete Lyapunov equations are of great importance but generally difficult to achieve in control system analysis and design. Fortunately, Mesbahi and Papavassilopoulos [On the rank minimization problems over a positive semidefinite linear matrix inequality, IEEE Trans. Auto. Control, Vol. 42, No. 2 (1997), 239-243] showed that with the semidefinite cone...

In this paper, we deal with second-order conic programming (SOCP) duals for a robust convex quadratic optimization problem uncertain data in the constraints. We first introduce SOCP dual polytopic sets. Then, obtain zero duality gap result between and its terms of new type characteristic cone constraint qualification. also construct norm-constrained sets corresponding them. Moreover, some numer...

We consider the problem of finding the nearest point in a polyhedral cone C = {x ∈ Rn : Dx ≤ 0} to a given point b ∈ Rn, where D ∈ Rm×n. This problem can be formulated as a convex quadratic programming problem with special structure. We study the structure of this problem and its relationship with the nearest point problem in a pos cone through the concept of polar cones. We then use this relat...

Nonconvex quadratic constraints can be linearized to obtain relaxations in a wellunderstood manner. We propose to tighten the relaxation by using second order cone constraints, resulting in a convex quadratic relaxation. Our quadratic approximation to the bilinear term is compared to the linear McCormick bounds. The second order cone constraints are based on linear combinations of pairs of vari...

Second-order cone programming (SOCP) is the problem of minimizing linear objective function over cross-section of second-order cones and an a ne space. Recently this problem gets more attention because of its various important applications including quadratically constrained convex quadratic programming. In this paper we deal with a primal-dual path-following algorithm for SOCP to show many of ...

Optimization problems are not only formed into a linear programming but also nonlinear programming. In real life, often decision variables restricted on integer. Hence, came the nonlinear programming. One particular form of nonlinear programming is a convex quadratic programming which form the objective function is quadratic and convex and linear constraint functions. In this research designed ...