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Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a sparse structure of input SDP by…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
In this paper, we consider the robust linear infinite programming problem $({\rm RLIP}_c) $ defined by \begin{eqnarray*} ({\rm RLIP}_c)\quad &&\inf\; \langle c,x\rangle \textrm{subject to } &&x\in X,\; \langle x^\ast,x \rangle \le r…
We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…
In this paper, we study the stochastic linear complementarity problems on extended second order cones (stochastic ESOCLCP). We first convert the problem to a stochastic mixed complementarity problem on the nonegative orthant (SMixCP).…
We present solutions to the matrix completion problems proposed by the Alignment Research Center that have a polynomial dependence on the precision $\varepsilon$. The motivation for these problems is to enable efficient computation of…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…
Uncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical LP paradigm. However, few of these are designed as extensions of the well-established and powerful CLP scheme…
Uncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical LP paradigm. However, few of these are designed as extensions of the well-established and powerful CLP scheme…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…
Although a unique solution is guaranteed in the Linear complementarity problem (LCP) when the matrix $\mathbf{M}$ is positive definite, practical applications often involve cases where $\mathbf{M}$ is only positive semi-definite, leading to…
The paper is dedicated to the study of strong duality for a problem of linear copositive programming. Based on the recently introduced concept of the set of normalized immobile indices, an extended dual problem is deduced. The dual problem…
We suppose the existence of an oracle which solves any semidefinite programming (SDP) problem satisfying Slater's condition simultaneously at its primal and dual sides. We note that such an oracle might not be able to directly solve general…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
An equivalence between attainability of simultaneous diagonalization (SD) and hidden convexity in quadratically constrained quadratic programming (QCQP) stimulates us to investigate necessary and sufficient SD conditions, which is one of…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
In semidefinite programming (SDP), unlike in linear programming, Farkas' lemma may fail to prove infeasibility. Here we obtain an exact, short certificate of infeasibility in SDP by an elementary approach: we reformulate any semidefinite…
Linear logic Concurrent Constraint programming (LCC) is an extension of concurrent constraint programming (CC) where the constraint system is based on Girard's linear logic instead of the classical logic. In this paper we address the…