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A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
The Densest Subgraph Problem (DSP) is widely used to identify community structures and patterns in networks such as bioinformatics and social networks. While solvable in polynomial time, traditional exact algorithms face computational and…
This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between…
In this paper, we propose two novel decentralized optimization frameworks for multi-agent nonlinear optimal control problems in robotics. The aim of this work is to suggest architectures that inherit the computational efficiency and…
We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity…
It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load…
In this article, we address a class of non convex, integer, non linear mathematical programs using dynamic programming. The mathematical program considered, whose properties are studied in this article, may be used to model the optimal…
Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the $\ell_1$ setting. We propose $(\varepsilon, \delta)$-DP algorithms based on stochastic mirror descent that attain nearly…
In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic…
Several well-known algorithms in the field of combinatorial optimization can be interpreted in terms of the primal-dual method for solving linear programs. For example, Dijkstra's algorithm, the Ford-Fulkerson algorithm, and the Hungarian…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Efficient nonlinearity compensation in fiber-optic communication systems is considered a key element to go beyond the "capacity crunch''. One guiding principle for previous work on the design of practical nonlinearity compensation schemes…
We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…
This paper proposes a general incremental policy iteration adaptive dynamic programming (ADP) algorithm for model-free robust optimal control of unknown nonlinear systems. The approach integrates recursive least squares estimation with…
We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our work generalizes the original Differential Dynamic Programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A…
This paper presents a novel extended dynamic programming approach for energy minimization (EDP) to solve the correspondence problem for stereo and motion. A significant speedup is achieved using a recursive minimum search strategy (RMS).…
The Double Linear Policy (DLP) framework guarantees a Robust Positive Expectation (RPE) under optimized constant-weight designs or admissible prespecified time-varying policies. However, the sequential optimization of these time-varying…