Related papers: A Unified Tool for Solving Uni-Parametric Linear P…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix $Q$ defining the quadratic term in the objective is sparse. We use a graphical representation of the support of $Q$, and show that if…
In this paper, we present a new geometric approach for sensitivity analysis in linear programming that is computationally practical for a decision-maker to study the behavior of the optimal solution of the linear programming problem under…
This paper proposes a new gradient method to solve the large-scale problems. Theoretical analysis shows that the new method has finite termination property for two dimensions and converges R-linearly for any dimensions. Experimental results…
In order to nd a non-negative solution to a system of inequalities, the corresponding dual problem is composed, which has a suitable unity basic matrix. In such a formulation, the objective function is replaced by set of constraints based…
A parametrized convex function depends on a variable and a parameter, and is convex in the variable for any valid value of the parameter. Such functions can be used to specify parametrized convex optimization problems, i.e., a convex…
This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…
Commutativity has proven to be a powerful tool in reasoning about concurrent programs. Recent work has shown that a commutativity-based reduction of a program may admit simpler proofs than the program itself. The framework of…
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…
This paper describes a program that solves elementary mathematical problems, mostly in metric space theory, and presents solutions that are hard to distinguish from solutions that might be written by human mathematicians. The program is…
We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
We propose a first-order method for convex optimization, where instead of being restricted to the gradient from a single parameter, gradients from multiple parameters can be used during each step of gradient descent. This setup is…
In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the…
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
We define quasiconvex programming, a form of generalized linear programming in which one seeks the point minimizing the pointwise maximum of a collection of quasiconvex functions. We survey algorithms for solving quasiconvex programs either…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…